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A279497 Number of pentagonal numbers dividing n. 3
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
Eric Weisstein's World of Mathematics, Pentagonal Number.
FORMULA
G.f.: Sum_{k>=1} x^(k*(3*k-1)/2)/(1 - x^(k*(3*k-1)/2)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*log(3) - Pi/sqrt(3) = 1.482037... (A244641). - Amiram Eldar, Jan 02 2024
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]]
Table[Count[Divisors[n], _?(IntegerQ[(1+Sqrt[1+24#])/6]&)], {n, 120}] (* Harvey P. Dale, Jan 05 2022 *)
PROG
(PARI) a(n) = sumdiv(n, d, ispolygonal(d, 5)); \\ Michel Marcus, Jul 27 2022
CROSSREFS
Sequence in context: A353445 A115722 A115721 * A359305 A138330 A128591
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 13 2016
STATUS
approved

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Last modified May 30 04:46 EDT 2024. Contains 372958 sequences. (Running on oeis4.)