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

Offset: 1

Author

Antti Karttunen, Jun 26 2024

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A328768, A373991 (characteristic function).

Union of A008591 and A374044.

Cf. A374042 (subsequence).

Cf. also A042965 (where A328768 is a multiple of 2), A327863 (where A003415 is a multiple of 3).

Programs

Mathematica

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

PARI

isA373992 = A373991;