A326394 - OEIS

%I #13 Jan 14 2024 02:28:19

%S 1,1,2,2,1,3,2,2,3,2,1,5,2,2,3,3,1,5,2,3,4,2,1,6,2,2,4,4,1,6,2,3,3,2,

%T 2,8,2,2,4,4,1,6,2,3,5,2,1,8,3,3,3,4,1,7,2,4,4,2,1,9,2,2,6,4,2,6,2,3,

%U 3,4,1,10,2,2,5,4,2,6,2,5,5,2,1,10,2,2,3,4,1,10,4

%N Expansion of Sum_{k>=1} x^k * (1 + x^(2*k)) / (1 - x^(3*k)).

%C Number of divisors of n that are not of the form 3*k + 2.

%F a(n) = A000005(n) - A001822(n).

%F Sum_{k=1..n} a(k) ~ 2*n*log(n)/3 + c*n, where c = (5*gamma-2)/3 - gamma(2,3) = (5*A001620-2)/3 - A256843 = 0.222152... . - _Amiram Eldar_, Jan 14 2024

%t nmax = 90; CoefficientList[Series[Sum[x^k (1 + x^(2 k))/(1 - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%t Table[DivisorSum[n, 1 &, !MemberQ[{2}, Mod[#, 3]] &], {n, 1, 90}]

%o (PARI) a(n) = {numdiv(n) - sumdiv(n, d, d%3==2)} \\ _Andrew Howroyd_, Sep 11 2019

%Y Cf. A000005, A001817, A001822, A003627, A032766, A035191, A082051, A326395.

%Y Cf. A001620, A256843.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Sep 11 2019