OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k>=1} k^2 * x^(k^2) * (1 + x^(k^2)) / (1 - x^(k^2))^3. - Ilya Gutkovskiy, Feb 21 2022
Multiplicative with a(p^e) = p^2*(p^(2*e) - p^(2*floor((e-1)/2)))/(p^2 - 1). - Sebastian Karlsson, Feb 25 2022
Sum_{k=1..n} a(k) ~ c * n^3, where c = zeta(4)/3 = Pi^4/270 = 0.360774... . - Amiram Eldar, Nov 13 2022
MATHEMATICA
f[p_, e_] := p^2*(p^(2*e) - p^(2*Floor[(e - 1)/2]))/(p^2 - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Nov 13 2022 *)
PROG
(PARI) a(n) = n^2*sumdiv(n, d, if (issquare(d), 1/d)); \\ Michel Marcus, Feb 15 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Wesley Ivan Hurt, Feb 14 2022
STATUS
approved