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 A279496 Number of square pyramidal numbers dividing n. 4
 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 2, 1, 1, 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, Square Pyramidal Number. Index to sequences related to pyramidal numbers. FORMULA G.f.: Sum_{k>=1} x^(k*(k+1)*(2*k+1)/6)/(1 - x^(k*(k+1)*(2*k+1)/6)). Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 18 - 24*log(2) = 1.364467... . - Amiram Eldar, Jan 02 2024 EXAMPLE a(10) = 2 because 10 has 4 divisors {1,2,5,10} among which 2 divisors {1,5} are square pyramidal numbers. MATHEMATICA Rest[CoefficientList[Series[Sum[x^(k (k + 1) (2 k + 1)/6)/(1 - x^(k (k + 1) (2 k + 1)/6)), {k, 120}], {x, 0, 120}], x]] CROSSREFS Cf. A000330, A046951. Sequence in context: A205007 A078470 A230799 * A151683 A133912 A277231 Adjacent sequences: A279493 A279494 A279495 * A279497 A279498 A279499 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Dec 13 2016 STATUS approved

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Last modified May 29 20:04 EDT 2024. Contains 372952 sequences. (Running on oeis4.)