A279496 Number of square pyramidal numbers dividing n.

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

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