A368363 Partial sums of A136107.

0, 1, 2, 3, 5, 6, 8, 9, 12, 13, 15, 17, 19, 21, 24, 25, 27, 30, 32, 34, 37, 39, 41, 43, 46, 48, 52, 53, 55, 59, 61, 62, 66, 68, 72, 74, 76, 78, 82, 84, 86, 90, 92, 94, 99, 101, 103, 105, 108, 111, 115, 117, 119, 123, 126, 128, 132, 134, 136, 140, 142, 144, 150, 151, 155, 158, 160, 162, 166, 170, 172, 175, 177, 179, 185

Offset

1,3

Comments

All three of A038548, A136107, and the present sequence have generating functions which resemble Lambert series.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, arXiv:2401.14346, Youtube

Formula

a(n) ~ n*(log(2*n)/2 + gamma - 1/2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jan 08 2024

Prog

(PARI) f(n) = numdiv(n>>valuation(n, 2)) - ispolygonal(n, 3); \\ A136107
a(n) = sum(k=1, n, f(k)); \\ Michel Marcus, Jan 08 2024

Crossrefs

Cf. A038548, A136107.

Sequence in context: A136112 A127936 A280771 * A348195 A280744 A331072

Adjacent sequences: A368360 A368361 A368362 * A368364 A368365 A368366

Keyword

nonn

Author

N. J. A. Sloane, Jan 08 2024

Status

approved