7-rough numbers

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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 corresponds to a prime sieve with eight candidates 30k+{1,7,11,13,17,19,23,29} = 30k-15±{14,8,4,2}.

See also

• Third row in an illustration for A002110, A005867, A038110, A060753.
• A084968 is the proper subset numbers with smallest prime factor 7.
• A098591 is a packed binary encoding of prime (1) vs. composite (0) 7-rough numbers.
• p-rough numbers

• 2-rough numbers
• 3-rough numbers
• 5-rough numbers
• 11-rough numbers
• 13-rough numbers
• 17-rough numbers
• 19-rough numbers
• 23-rough numbers