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A279497 Number of pentagonal numbers dividing n. 1
1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 4, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 2, 1, 3, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..120.

Eric Weisstein's World of Mathematics, Pentagonal Number

Index to sequences related to polygonal numbers

FORMULA

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

EXAMPLE

a(12) = 2 because 12 has 6 divisors {1,2,3,4,6,12} among which 2 divisors {1,12} are pentagonal numbers.

MATHEMATICA

Rest[CoefficientList[Series[Sum[x^(k (3k -1)/2)/(1 - x^(k (3k -1)/2)), {k, 120}], {x, 0, 120}], x]]

CROSSREFS

Cf. A000326, A007862, A046951.

Sequence in context: A063993 A115722 A115721 * A138330 A128591 A254444

Adjacent sequences:  A279494 A279495 A279496 * A279498 A279499 A279500

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Dec 13 2016

STATUS

approved

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Last modified July 24 01:23 EDT 2021. Contains 346269 sequences. (Running on oeis4.)