Kiinnostavia alkulukuaiheisia kokonaislukujonoja

Tällä sivulla on kiinnostavia alkulukuaiheisia kokonaislukuja, jotka voidaan kuvata yksinkertaisena joukkona. Olen kopioinut ne The On-Line Encyclopedia of Integer Sequences® (OEIS®) -sivustolta mutta olen kirjoittanut kaavat itse. (Mukana on joitakin muitakin perustavanlaatuisia lukujonoja, kuten positiiviset kokonaisluvut.)

Huomautuksia

Sisällysluettelo

Tasan yksi alkutekijä

OEIS kaa­va al­ku­pe­räi­nen ku­vaus en­sim­mäi­set al­kiot
A000040 {p} The prime numbers. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97

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OEIS kaa­va al­ku­pe­räi­nen ku­vaus en­sim­mäi­set al­kiot
A001248 {p2} Squares of primes. 4,9,25,49,121,169,289,361,529,841,961,1369,1681,1849,2209,2809,3481
A006881 {pq} Squarefree semiprimes: Numbers that are the product of two distinct primes. 6,10,14,15,21,22,26,33,34,35,38,39,46,51,55,57,58,62,65,69,74,77,82,85
A001358 {pq, p2} Semiprimes (or biprimes): products of two primes. 4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,51,55,57,58,62,65,69

Tasan kolme alkutekijää

OEIS kaa­va al­ku­pe­räi­nen ku­vaus en­sim­mäi­set al­kiot
A030078 {p3} Cubes of primes. 8,27,125,343,1331,2197,4913,6859,12167,24389,29791,50653,68921,79507
A054753 {p2q} Numbers which are the product of a prime and the square of a different prime. 12,18,20,28,44,45,50,52,63,68,75,76,92,98,99,116,117,124,147,148,153
A285508 {p2q, p3} Numbers with exactly three prime factors, not all distinct. 8,12,18,20,27,28,44,45,50,52,63,68,75,76,92,98,99,116,117,124,125,147
A007304 {pqr} Sphenic numbers: products of 3 distinct primes. 30,42,66,70,78,102,105,110,114,130,138,154,165,170,174,182,186,190,195
A217856 {pqr, p2q} Numbers with three prime factors, not necessarily distinct, except cubes of primes. 12,18,20,28,30,42,44,45,50,52,63,66,68,70,75,76,78,92,98,99,102,105
A014612 {pqr, p2q, p3} Numbers that are the product of exactly three (not necessarily distinct) primes. 8,12,18,20,27,28,30,42,44,45,50,52,63,66,68,70,75,76,78,92,98,99,102

Tasan neljä alkutekijää (enintään kolme erilaista)

OEIS kaa­va al­ku­pe­räi­nen ku­vaus en­sim­mäi­set al­kiot
A030514 {p4} 4th powers of primes. 16,81,625,2401,14641,28561,83521,130321,279841,707281,923521,1874161
A065036 {p3q} Product of the cube of a prime (A030078) and a different prime. 24,40,54,56,88,104,135,136,152,184,189,232,248,250,296,297,328,344,351
A085986 {p2q2} Squares of the squarefree semiprimes. 36,100,196,225,441,484,676,1089,1156,1225,1444,1521,2116,2601,3025
A085987 {p2qr} Product of exactly four primes, three of which are distinct. 60,84,90,126,132,140,150,156,198,204,220,228,234,260,276,294,306,308

Tasan viisi alkutekijää (enintään kolme erilaista)

OEIS kaa­va al­ku­pe­räi­nen ku­vaus en­sim­mäi­set al­kiot
A050997 {p5} Fifth powers of primes. 32,243,3125,16807,161051,371293,1419857,2476099,6436343,20511149
A178739 {p4q} Product of the 4th power of a prime (A030514) and a different prime. 48,80,112,162,176,208,272,304,368,405,464,496,567,592,656,688,752,848
A143610 {p3q2} Numbers of the form p^2*q^3, where p,q are distinct primes. 72,108,200,392,500,675,968,1125,1323,1352,1372,2312,2888,3087,3267
A189975 {p3qr} Numbers with prime factorization pqr^3. 120,168,264,270,280,312,378,408,440,456,520,552,594,616,680,696,702
A179643 {p2q2r} Products of exactly 2 distinct primes squares and a different prime (p^2*q^2*r). 180,252,300,396,450,468,588,612,684,700,828,882,980,1044,1100,1116

Tasan kuusi alkutekijää (enintään kolme erilaista)

OEIS kaa­va al­ku­pe­räi­nen ku­vaus en­sim­mäi­set al­kiot
A030516 {p6} Numbers with 7 divisors. 64,729,15625,117649,1771561,4826809,24137569,47045881,148035889
A178740 {p5q} Product of the 5th power of a prime (A050997) and a different prime. 96,160,224,352,416,486,544,608,736,928,992,1184,1215,1312,1376,1504
A189988 {p4q2} Numbers with prime factorization p^2*q^4. 144,324,400,784,1936,2025,2500,2704,3969,4624,5625,5776,8464,9604,9801
A179644 {p4qr} Product of the 4th power of a prime and 2 different distinct primes (p^4*q*r). 240,336,528,560,624,810,816,880,912,1040,1104,1134,1232,1360,1392,1456
A162142 {p3q3} Numbers that are the cube of a product of two distinct primes. 216,1000,2744,3375,9261,10648,17576,35937,39304,42875,54872,59319
A163569 {p3q2r} Numbers of the form p^3*q^2*r where p, q and r are three distinct primes. 360,504,540,600,756,792,936,1176,1188,1224,1350,1368,1400,1404,1500
A162143 {p2q2r2} a(n) = A007304(n)^2. 900,1764,4356,4900,6084,10404,11025,12100,12996,16900,19044,23716

Tasan yksi eri alkutekijä

OEIS kaa­va al­ku­pe­räi­nen ku­vaus en­sim­mäi­set al­kiot
A000430 {p, p2} Primes and squares of primes. 2,3,4,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49,53,59,61,67,71,73
A168363 {p2, p3} Squares and cubes of primes. 4,8,9,25,27,49,121,125,169,289,343,361,529,841,961,1331,1369,1681,1849
A087797 {p, p2, p3} Primes, squares of primes and cubes of primes. 2,3,4,5,7,8,9,11,13,17,19,23,25,27,29,31,37,41,43,47,49,53,59,61,67,71
A246655 {pn} Prime powers: Numbers of the form p^k where p is a prime and k >= 1. 2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43,47,49,53,59,61
A246547 {pn} (n ≥ 2) Prime powers p^e where p is a prime and e >= 2 (prime powers without the primes or 1). 4,8,9,16,25,27,32,49,64,81,121,125,128,169,243,256,289,343,361,512,529
A246549 {pn} (n ≥ 3) Prime powers p^e where p is a prime and e >= 3 (prime powers without 1, the primes, or the squares of primes). 8,16,27,32,64,81,125,128,243,256,343,512,625,729,1024,1331,2048,2187
A051674 {pp} a(n) = prime(n)^prime(n). 4,27,3125,823543,285311670611,302875106592253,827240261886336764177
A257278 {pn} (np) Prime powers p^m with p <= m. 4,8,16,27,32,64,81,128,243,256,512,729,1024,2048,2187,3125,4096,6561
A192135 {pn} (n > p) Prime powers p^e with p < e. 8,16,32,64,81,128,243,256,512,729,1024,2048,2187,4096,6561,8192,15625
A053810 {pp, pq} Prime powers of prime numbers. 4,8,9,25,27,32,49,121,125,128,169,243,289,343,361,529,841,961,1331

Tasan kaksi eri alkutekijää

OEIS kaa­va al­ku­pe­räi­nen ku­vaus en­sim­mäi­set al­kiot
A084227 {pnq} Numbers of the form p*q^k with distinct primes p and q, k>0. 6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,38,39,40,44,45,46,48,50,51
A007774 {pnqm} Numbers that are divisible by exactly 2 different primes. 6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,36,38,39,40,44,45,46,48,50

Muita

OEIS kaa­va al­ku­pe­räi­nen ku­vaus en­sim­mäi­set al­kiot
A000027 {n} The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous. 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26
A005117 {1, p, pq, …} Squarefree numbers: numbers that are not divisible by a square greater than 1. 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,30,31,33,34,35,37,38
A062503 {1, p2, p2q2, …} Squarefree numbers squared. 1,4,9,25,36,49,100,121,169,196,225,289,361,441,484,529,676,841,900,961
A062838 {1, p3, p3q3, …} Cubes of squarefree numbers. 1,8,27,125,216,343,1000,1331,2197,2744,3375,4913,6859,9261,10648,12167
A004709 {1, pn, pnqm, …} (n, m, … ≤ 2) Cubefree numbers: numbers that are not divisible by any cube > 1. 1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,25,26,28,29,30
A013929 {p2n} Numbers that are not squarefree. Numbers that are divisible by a square greater than 1. The complement of A005117. 4,8,9,12,16,18,20,24,25,27,28,32,36,40,44,45,48,49,50,52,54,56,60,63
A046099 {p3n} Numbers that are not cubefree. Numbers divisible by a cube greater than 1. Complement of A004709. 8,16,24,27,32,40,48,54,56,64,72,80,81,88,96,104,108,112,120,125,128
A002808 {pqn, p2n} The composite numbers: numbers n of the form x*y for x > 1 and y > 1. 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38