A373992 - OEIS

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A373992

Numbers k such that A328768(k) is a multiple of 3, where A328768 is the first primorial based variant of arithmetic derivative.

0, 1, 5, 7, 8, 9, 11, 13, 17, 18, 19, 23, 25, 27, 29, 31, 35, 36, 37, 40, 41, 43, 45, 47, 49, 53, 54, 55, 56, 59, 61, 63, 64, 65, 67, 71, 72, 73, 77, 79, 81, 83, 85, 88, 89, 90, 91, 95, 97, 99, 101, 103, 104, 107, 108, 109, 113, 115, 117, 119, 121, 125, 126, 127, 131, 133, 135, 136, 137, 139, 143, 144, 145, 149

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OFFSET

1,3

COMMENTS

Term is present if and only if it is either a multiple of 9, or it is not a multiple of 3 but its 2-adic valuation is (a multiple of 3).

A multiplicative semigroup: if m and n are in the sequence, then so is m*n.

The asymptotic density of this sequence is 31/63. - Amiram Eldar, Jun 28 2024

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..12000

Index entries for sequences related to primorial numbers.

MATHEMATICA

Select[Range[0, 150], Divisible[#, 9] || (!Divisible[#, 3] && Divisible[IntegerExponent[#, 2], 3]) &] (* Amiram Eldar, Jun 28 2024 *)