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

Author

N. J. A. Sloane, Nov 04 2018

Keywords

• nonn
• easy

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

Crossrefs

Cf. A000005, A001620, A321015.

A072527 is a shifted version.

Column k=4 of A135539.

Programs

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 *)

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

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