5-rough numbers

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Least prime factor   ≥   5. Numbers congruent to 1 or 5 mod 6.

Sequences

A007310 5-rough numbers: positive integers that have no prime factors less than 5.

{1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 121, 125, ...}

If

a (n)

is the

n

-th 5-rough number then

a (n) ∼ 3n

. In fact, more is true:

a (n) = 3 n + O (1)

.

See also

• Second row in an illustration for A002110, A005867, A038110, A060753.
• A084967 is the proper subset numbers with smallest prime factor 5.
• p-rough numbers

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