OFFSET
1,5
LINKS
Eric Weisstein's World of Mathematics, Square Pyramidal Number.
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
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 13 2016
STATUS
approved