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

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

Prog

(PARI) ist(n) = my(k=sqrtnint(6*n, 3)); k*(k+1)*(k+2)==6*n; \\ A000292
a(n) = sumdiv(n, d, if (ist(d), d)); \\ Michel Marcus, May 19 2020

Crossrefs

Cf. A000292, A023533, A068980, A185027, A279495, A334987.

Sequence in context: A250131 A100615 A293897 * A334987 A222119 A351086

Adjacent sequences: A334985 A334986 A334987 * A334989 A334990 A334991

Keyword

nonn,changed

Author

Ilya Gutkovskiy, May 18 2020

Status

approved