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# 7-rough numbers

From OeisWiki

Least prime factor ≥ 7.

## Sequences

A007775 7-rough numbers: positive integers that have no prime factors less than 7.

- {1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 119, 121, 127, 131, 133, 137, 139, 143, 149, ...}

In every block of 30 consecutive integers, there are exactly eight 7-rough numbers, so this sequence has natural density 8/30 = 4/15 = 0.2666....

This sequence corresponds to a prime sieve consisting of 8 candidates[30 k + 1, 30 k + 7, 30 k + 11, 30 k + 13, 30 k + 17, 30 k + 19, 30 k + 23, 30 k + 29] |

[30 k, 30 k + 29] |

## See also

- Third row in an illustration for A002110, A005867, A038110, A060753.
- A084968 is the proper subset
*numbers with smallest prime factor 7*. -
*p*-rough numbers