OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
FORMULA
a(n) = Sum_{d|n} d*A001221(d).
a(n) = Sum_{d|n} (n/d) * sopf(d). - Wesley Ivan Hurt, May 24 2021
Dirichlet g.f.: primezeta(s-1) * zeta(s-1) * zeta(s). - Ilya Gutkovskiy, Aug 18 2021
Conjecture: Sum_{k=1..n} a(k) ~ Pi^2 * n^2 * (log(log(n)) + A077761) / 12. - Vaclav Kotesovec, Mar 03 2023
MATHEMATICA
Table[Sum[d*PrimeNu[d], {d, Divisors[n]}], {n, 1, 100}] (* Vaclav Kotesovec, Aug 18 2021 *)
PROG
(PARI) A329354(n) = sumdiv(n, d, omega(d)*d);
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 15 2019
STATUS
approved