A338652 Number of divisors of n which are greater than 8.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 3, 2, 1, 4, 1, 3, 2, 3, 1, 4, 2, 3, 2, 2, 1, 6, 1, 2, 3, 3, 2, 4, 1, 3, 2, 4, 1, 6, 1, 2, 3, 3, 2, 4, 1, 5, 3, 2, 1, 6, 2, 2, 2, 4, 1, 7, 2, 3, 2, 2, 2, 6, 1, 3, 4, 5, 1, 4, 1, 4, 4, 2, 1, 7, 1, 5

Offset

1,18

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Index entries for sequences related to divisors of numbers.

Formula

G.f.: Sum_{k>=1} x^(9*k) / (1 - x^k).

L.g.f.: -log( Product_{k>=9} (1 - x^k)^(1/k) ).

G.f.: Sum_{k>=9} x^k/(1 - x^k). - Seiichi Manyama, Jan 07 2023

Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 1041/280), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 08 2024

Mathematica

Table[DivisorSum[n, 1 &, # > 8 &], {n, 1, 110}]
nmax = 110; CoefficientList[Series[Sum[x^(9 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 1] &
nmax = 110; CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 9, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Drop[#, 1] &

Prog

(PARI) a(n) = sumdiv(n, d, d>8); \\ Michel Marcus, Apr 22 2021
(PARI) my(N=100, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0, 0, 0], Vec(sum(k=9, N, x^k/(1-x^k)))) \\ Seiichi Manyama, Jan 07 2023

Crossrefs

Column k=9 of A135539.

Cf. A000005, A001620, A023645, A032741, A321014, A338648, A338649, A338650, A338651, A338653.

Sequence in context: A376885 A099305 A334461 * A033109 A321469 A365460

Adjacent sequences: A338649 A338650 A338651 * A338653 A338654 A338655

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Apr 22 2021

Extensions

a(1)-a(8) prepended by David A. Corneth, Jun 13 2022

Status

approved