OFFSET
1,8
COMMENTS
Inverse Moebius transform of A046660.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k>=1} A046660(k) * x^k / (1 - x^k).
If m and n are coprime, a(m*n) = tau(m)*a(n) + tau(n)*a(m), where tau = A000005. - Robert Israel, Jun 12 2020
MAPLE
N:= 100: # for a(1)..a(N)
V:= Vector(N):
for d from 1 to N do
v:= add(t[2]-1, t=ifactors(d)[2]);
L:= [seq(i, i=d..N, d)]:
V[L]:= map(`+`, V[L], v);
od:
convert(V, list); # Robert Israel, Jun 12 2020
MATHEMATICA
a[n_] := Sum[PrimeOmega[d] - PrimeNu[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 90}]
PROG
(PARI) a(n) = sumdiv(n, d, bigomega(d) - omega(d)); \\ Michel Marcus, Jun 12 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 27 2019
STATUS
approved