OFFSET
1,2
FORMULA
Multiplicative with a(p^e) = ((p^(e+1)-1)/(p-1))^3.
Dirichlet g.f.: zeta(s) * zeta(s-1) * zeta(s-2) * zeta(s-3) * Product_{primes p} (1 + 1/p^(2*s-3) + 2/p^(s-1) + 2/p^(s-2)).
Sum_{k=1..n} a(k) ~ c * Pi^6 * zeta(3) * n^4 / 2160, where c = Product_{primes p} (1 + 2/p^2 + 2/p^3 + 1/p^5) = 2.83598357433419286770442457158038489640898183...
MATHEMATICA
Table[DivisorSigma[1, n]^3, {n, 1, 50}]
PROG
(PARI) a(n) = sigma(n)^3;
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 + p*X*(2 + 2*p + p^2*X)) / ((1-X)*(1-p*X)*(1-p^2*X)*(1-p^3*X)))[n], ", "))
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Vaclav Kotesovec, Mar 02 2023
STATUS
approved