A338648 Number of divisors of n which are greater than 4.

0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 2, 3, 1, 5, 1, 3, 2, 2, 3, 5, 1, 2, 2, 5, 1, 5, 1, 3, 4, 2, 1, 6, 2, 4, 2, 3, 1, 5, 3, 5, 2, 2, 1, 8, 1, 2, 4, 4, 3, 5, 1, 3, 2, 6, 1, 8, 1, 2, 4, 3, 3, 5, 1, 7, 3, 2, 1, 8, 3, 2, 2, 5, 1, 9, 3, 3, 2, 2, 3, 8, 1, 4, 4, 6, 1, 5, 1, 5, 6, 2, 1, 8, 1, 6

Offset

1,10

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^(5*k) / (1 - x^k).

L.g.f.: -log( Product_{k>=5} (1 - x^k)^(1/k) ).

a(n) = A000005(n) - A083040(n).

G.f.: Sum_{k>=5} x^k/(1 - x^k). - Seiichi Manyama, Jan 07 2023

Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 37/12), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 08 2024

Mathematica

Table[DivisorSum[n, 1 &, # > 4 &], {n, 1, 110}]
nmax = 110; CoefficientList[Series[Sum[x^(5 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, 5, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Drop[#, 1] &

Prog

(PARI) a(n) = sumdiv(n, d, d>4); \\ Michel Marcus, Apr 22 2021; corrected Jun 13 2022
(PARI) my(N=100, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(sum(k=5, N, x^k/(1-x^k)))) \\ Seiichi Manyama, Jan 07 2023

Crossrefs

Column k=5 of A135539.

Cf. A000005, A001620, A023645, A032741, A083040, A321014, A338649, A338650, A338651, A338652, A338653.

Sequence in context: A348955 A062362 A330437 * A269252 A291150 A292375

Adjacent sequences: A338645 A338646 A338647 * A338649 A338650 A338651

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Apr 22 2021

Extensions

a(1)-a(4) prepended by David A. Corneth, Jun 13 2022

Status

approved