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

Author

N. J. A. Sloane, Jan 08 2024

Keywords

• nonn

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

Crossrefs

Cf. A038548, A136107.

Programs

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

Formula

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