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

Author

Ilya Gutkovskiy, Dec 13 2016

Keywords

• nonn
• easy

Examples

			a(10) = 2 because 10 has 4 divisors {1,2,5,10} among which 2 divisors {1,5} are square pyramidal numbers.
		

Links

• Eric Weisstein's World of Mathematics, Square Pyramidal Number.
• Index to sequences related to pyramidal numbers.

Crossrefs

Cf. A000330, A046951.

Programs

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]]

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