A321014 Number of divisors of n which are greater than 3.

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

Offset

1,8

References

Marjorie Senechal, "Introduction to lattice geometry." In M. Waldschmidt et al., eds., From Number Theory to Physics, pp. 476-495. Springer, Berlin, Heidelberg, 1992. See Cor. 3.7.

Links

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

Formula

G.f.: Sum_{k>=4} x^k/(1 - x^k). - Ilya Gutkovskiy, Nov 06 2018

a(n) = Sum_{d|n, d>3} 1. - Wesley Ivan Hurt, Apr 28 2020

G.f.: Sum_{k>=1} x^(4*k)/(1 - x^k). - Seiichi Manyama, Jan 07 2023

Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 17/6), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 08 2024

Maple

d2:=proc(n) local c;
if n <= 3 then return(0); fi;
c:=NumberTheory[tau](n)-1;
if (n mod 2)=0 then c:=c-1; fi;
if (n mod 3)=0 then c:=c-1; fi; c; end;
[seq(d2(n), n=1..120)];

Mathematica

nmax = 94; Rest[CoefficientList[Series[Sum[x^k/(1 - x^k), {k, 4, nmax}], {x, 0, nmax}], x]] (* Ilya Gutkovskiy, Nov 07 2018 *)

Prog

(PARI) a(n) = sumdiv(n, d, d>3); \\ Michel Marcus, Nov 06 2018
(PARI) a(n) = numdiv(n) - 3 + !!(n%2) + !!(n%3) \\ David A. Corneth, Nov 07 2018
(PARI) my(N=100, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, x^(4*k)/(1-x^k)))) \\ Seiichi Manyama, Jan 07 2023

Crossrefs

Cf. A000005, A001620, A321015.

A072527 is a shifted version.

Column k=4 of A135539.

Sequence in context: A329312 A211271 A124768 * A072527 A345138 A343945

Adjacent sequences: A321011 A321012 A321013 * A321015 A321016 A321017

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 04 2018

Status

approved