|
|
A330018
|
|
a(n) = Sum_{d|n} (bigomega(d) - omega(d)).
|
|
1
|
|
|
0, 0, 0, 1, 0, 0, 0, 3, 1, 0, 0, 2, 0, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 6, 1, 0, 3, 2, 0, 0, 0, 10, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 0, 12, 1, 2, 0, 2, 0, 6, 0, 6, 0, 0, 0, 4, 0, 0, 2, 15, 0, 0, 0, 2, 0, 0, 0, 13, 0, 0, 2, 2, 0, 0, 0, 12, 6, 0, 0, 4, 0, 0, 0, 6, 0, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,8
|
|
COMMENTS
|
Inverse Moebius transform of A046660.
|
|
LINKS
|
|
|
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:
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|