A334987 Sum of centered triangular numbers dividing n.

1, 1, 1, 5, 1, 1, 1, 5, 1, 11, 1, 5, 1, 1, 1, 5, 1, 1, 20, 15, 1, 1, 1, 5, 1, 1, 1, 5, 1, 11, 32, 5, 1, 1, 1, 5, 1, 20, 1, 15, 1, 1, 1, 5, 1, 47, 1, 5, 1, 11, 1, 5, 1, 1, 1, 5, 20, 1, 1, 15, 1, 32, 1, 69, 1, 1, 1, 5, 1, 11, 1, 5, 1, 1, 1, 24, 1, 1, 1, 15, 1, 1, 1, 5, 86, 1, 1, 5, 1, 11

Offset

1,4

Links

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

Eric Weisstein's World of Mathematics, Centered Triangular Number

Formula

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

L.g.f.: log(G(x)), where G(x) is the g.f. for A280950.

Mathematica

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

Prog

(PARI) isc(n) = my(k=(2*n-2)/3, m); (n==1) || ((denominator(k)==1) && (m=sqrtint(k)) && (m*(m+1)==k));
a(n) = sumdiv(n, d, if (isc(d), d)); \\ Michel Marcus, May 19 2020

Crossrefs

Cf. A005448, A185027, A280950, A300409, A334988.

Sequence in context: A100615 A293897 A334988 * A222119 A351086 A102280

Adjacent sequences: A334984 A334985 A334986 * A334988 A334989 A334990

Keyword

nonn

Author

Ilya Gutkovskiy, May 18 2020

Status

approved