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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 04 2018
STATUS
approved