A373138 Numbers k such that A276085(k) is a multiple of 8, where A276085 is the primorial base log-function.

1, 15, 20, 21, 28, 39, 51, 52, 55, 57, 68, 76, 77, 81, 87, 93, 108, 115, 116, 124, 141, 143, 144, 161, 183, 185, 187, 188, 192, 201, 205, 209, 215, 219, 225, 237, 244, 256, 259, 265, 267, 268, 287, 291, 292, 295, 297, 299, 300, 301, 303, 309, 315, 316, 319, 327, 339, 341, 355, 356, 371, 381, 388, 391, 396, 400, 404

Offset

1,2

Comments

Because A276085 is completely additive, this is a multiplicative semigroup; if m and n are in the sequence then so is m*n.

The terms should be the integers in a multiplicative subgroup of the positive rationals. Denoting the k-th prime by p_k, a set of generators for this subgroup might be the union of {20, 81} with an infinite set constituted as follows: if p_k == 3 (mod 4) then p_k * p_{k+1} is in the set, if p_k == 1 (mod 4) then p_k^3 * p_{k+1} is in the set. - Peter Munn, Jul 15 2024

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to primorial numbers

Prog

(PARI) \\ See A373137.

Crossrefs

Cf. A002110, A276085, A373137 (characteristic function).

Subsequence of A369002.

Cf. A373259 (subsequence).

Sequence in context: A330522 A171808 A134617 * A113529 A378368 A214410

Adjacent sequences: A373135 A373136 A373137 * A373139 A373140 A373141

Keyword

nonn

Author

Antti Karttunen, May 26 2024

Status

approved