# interesting prime-related integer sequences

Here are some integer sequences from The On-Line Encyclopedia of Integer Sequences that can be easily expressed as a set.

`p`, `q`, `r` and `s` denote distinct primes.

## one prime factor

OEIS | formula | OEIS description | first items |
---|---|---|---|

`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 |

## two prime factors

OEIS | formula | OEIS description | first items |
---|---|---|---|

`A001248` |
{p^{2}} |
Squares of primes. |
4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809 |

`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 |

## three prime factors

OEIS | formula | OEIS description | first items |
---|---|---|---|

`A030078` |
{p^{3}} |
Cubes of primes. |
8, 27, 125, 343, 1331, 2197, 4913, 6859, 12167, 24389, 29791, 50653, 68921 |

`A054753` |
{p^{2}q} |
Numbers which are the product of a prime and the square of a different prime (p^2 * q). |
12, 18, 20, 28, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99, 116, 117, 124, 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 |

## four prime factors

OEIS | formula | OEIS description | first items |
---|---|---|---|

`A030514` |
{p^{4}} |
4th powers of primes. |
16, 81, 625, 2401, 14641, 28561, 83521, 130321, 279841, 707281, 923521, 1874161 |

`A065036` |
{p^{3}q} |
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 |

`A085986` |
{p^{2}q^{2}} |
Squares of the squarefree semiprimes (p^2*q^2). |
36, 100, 196, 225, 441, 484, 676, 1089, 1156, 1225, 1444, 1521, 2116, 2601, 3025 |

`A046386` |
{pqrs} |
Products of four distinct primes. |
210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 858, 870, 910, 930, 966 |