OFFSET
1,6
COMMENTS
Number of divisors of n that are not of the form 3*k + 1.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{k=1..n} a(k) ~ 2*n*log(n)/3 + c*n, where c = (5*gamma-2)/3 - gamma(1,3) = (5*A001620-2)/3 - A256425 = -0.382447... . - Amiram Eldar, Jan 14 2024
MAPLE
N:= 100: # for a(1) .. a(N)
S:= series(add(x^(2*k)*(1+x^k)/(1-x^(3*k)), k=1..N/2), x, N+1):
seq(coeff(S, x, i), i=1..N); # Robert Israel, Aug 27 2020
MATHEMATICA
nmax = 90; CoefficientList[Series[Sum[x^(2 k) (1 + x^k)/(1 - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, 1 &, !MemberQ[{1}, Mod[#, 3]] &], {n, 1, 90}]
PROG
(PARI) a(n) = {numdiv(n) - sumdiv(n, d, d%3==1)} \\ Andrew Howroyd, Sep 11 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 11 2019
STATUS
approved