A334926 - OEIS

%I #10 Jan 02 2024 02:46:00

%S 1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,2,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,

%T 1,2,1,2,1,1,1,2,1,2,1,1,1,2,1,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,1,2,1,1,

%U 1,1,1,2,1,1,1,2,1,2,1,1,1,1,1,2,2,1,1,2,1,2,1,1,1,1,2,2,1,1,1,1

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

%C Number of octahedral numbers (A005900) dividing n.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OctahedralNumber.html">Octahedral Number</a>.

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A175577 = 1.278185... . - _Amiram Eldar_, Jan 02 2024

%t nmax = 100; CoefficientList[Series[Sum[x^(k (2 k^2 + 1)/3)/(1 - x^(k (2 k^2 + 1)/3)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A005900, A061704, A175577, A279495, A279496, A300410, A334925.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, May 16 2020