OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} tau(n * d^2) = Sum_{d|n} tau(n^2).
a(n) = tau(n) * tau(n^2).
G.f.: Sum_{k>=1} tau(k^4) * x^k/(1 - x^k).
Multiplicative with a(p^e) = 2*e^2 + 3*e + 1. - Amiram Eldar, Dec 14 2022
MATHEMATICA
Array[DivisorSum[#, DivisorSigma[0, #^4] &] &, 120] (* Michael De Vlieger, Dec 13 2022 *)
f[p_, e_] := 2*e^2 + 3*e + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Dec 14 2022 *)
PROG
(PARI) a(n) = sumdiv(n, d, numdiv(d^4));
(PARI) a(n) = sumdiv(n, d, numdiv(n*d^2));
(PARI) a(n) = sumdiv(n, d, numdiv(n^2));
(PARI) a(n) = numdiv(n)*numdiv(n^2);
(PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=1, N, numdiv(k^4)*x^k/(1-x^k)))
(Python)
from math import prod
from sympy import factorint
def A356574(n): return prod((e+1)*((e<<1)+1) for e in factorint(n).values()) # Chai Wah Wu, Dec 13 2022
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Seiichi Manyama, Dec 13 2022
STATUS
approved