A334988 - OEIS

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A334988

Sum of tetrahedral numbers dividing n.

1, 1, 1, 5, 1, 1, 1, 5, 1, 11, 1, 5, 1, 1, 1, 5, 1, 1, 1, 35, 1, 1, 1, 5, 1, 1, 1, 5, 1, 11, 1, 5, 1, 1, 36, 5, 1, 1, 1, 35, 1, 1, 1, 5, 1, 1, 1, 5, 1, 11, 1, 5, 1, 1, 1, 61, 1, 1, 1, 35, 1, 1, 1, 5, 1, 1, 1, 5, 1, 46, 1, 5, 1, 1, 1, 5, 1, 1, 1, 35, 1, 1, 1, 89, 1, 1, 1, 5, 1, 11

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..90.

Eric Weisstein's World of Mathematics, Tetrahedral Number

FORMULA

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

L.g.f.: log(G(x)), where G(x) is the g.f. for A068980.

a(n) = Sum_{d|n} A023533(d) * d.

MATHEMATICA

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