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A334926
G.f.: Sum_{k>=1} x^(k*(2*k^2 + 1)/3) / (1 - x^(k*(2*k^2 + 1)/3)).
1
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, 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, 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
OFFSET
1,6
COMMENTS
Number of octahedral numbers (A005900) dividing n.
LINKS
Eric Weisstein's World of Mathematics, Octahedral Number.
FORMULA
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A175577 = 1.278185... . - Amiram Eldar, Jan 02 2024
MATHEMATICA
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 16 2020
STATUS
approved