OFFSET
1,2
COMMENTS
For background references see A330570.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
E. C. Titchmarsh, Some problems in the analytic theory of numbers, The Quarterly Journal of Mathematics, Vol. 1 (1942), pp. 129-152.
FORMULA
a(n) ~ c * n * log(n)^5 /5!, where c = Product_{p prime} ((1-1/p)^2*(1+2/p)) = 0.286747428434478734107... (Titchmarsh, 1942). - Amiram Eldar, Apr 19 2024
MATHEMATICA
f[p_, e_] := (e+1)^2*(e+2)/2; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Accumulate[Array[s, 100]] (* Amiram Eldar, Apr 19 2024 *)
PROG
(PARI) lista(nmax) = {my(s = 0); for(n = 1, nmax, s += vecprod(apply(e -> (e+1)^2*(e+2)/2, factor(n)[, 2])); print1(s, ", ")); } \\ Amiram Eldar, Apr 19 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 10 2020
STATUS
approved