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

1,3

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 *)

Prog

(PARI) isA373992 = A373991;

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).

Sequence in context: A118742 A122904 A104693 * A225648 A031221 A137469

Adjacent sequences: A373989 A373990 A373991 * A373993 A373994 A373995

Keyword

nonn,easy

Author

Antti Karttunen, Jun 26 2024

Status

approved