OFFSET
1,2
FORMULA
a(n) = Sum_{d|n} tau(n * d^5) = Sum_{d|n} tau(n^2 * d^3) = Sum_{d|n} tau(n^3 * d) = Sum_{d|n} tau(n^4 / d).
G.f.: Sum_{k>=1} tau(k^7) * x^k/(1 - x^k).
Multiplicative with a(p^e) = 7*e^2/2 + 9*e/2 + 1. - Amiram Eldar, Dec 14 2022
MATHEMATICA
Array[DivisorSum[#, DivisorSigma[0, #^7] &] &, 120] (* Michael De Vlieger, Dec 13 2022 *)
f[p_, e_] := 7*e^2/2 + 9*e/2 + 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^7));
(PARI) a(n) = sumdiv(n, d, numdiv(n*d^5));
(PARI) a(n) = sumdiv(n, d, numdiv(n^2*d^3));
(PARI) a(n) = sumdiv(n, d, numdiv(n^3*d));
(PARI) a(n) = sumdiv(n, d, numdiv(n^4/d));
(PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=1, N, numdiv(k^7)*x^k/(1-x^k)))
(Python)
from math import prod
from sympy import factorint
def A359038(n): return prod((e+1)*(7*e+2)>>1 for e in factorint(n).values()) # Chai Wah Wu, Dec 13 2022
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
Seiichi Manyama, Dec 13 2022
STATUS
approved