|
|
A349441
|
|
Dirichlet convolution of A057521 (powerful part of n) with A055615 (Dirichlet inverse of n).
|
|
4
|
|
|
1, -1, -2, 2, -4, 2, -6, 0, 6, 4, -10, -4, -12, 6, 8, 0, -16, -6, -18, -8, 12, 10, -22, 0, 20, 12, 0, -12, -28, -8, -30, 0, 20, 16, 24, 12, -36, 18, 24, 0, -40, -12, -42, -20, -24, 22, -46, 0, 42, -20, 32, -24, -52, 0, 40, 0, 36, 28, -58, 16, -60, 30, -36, 0, 48, -20, -66, -32, 44, -24, -70, 0, -72, 36, -40, -36
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Multiplicative with a(p^e) = 1 - p is e = 1, p^2 - p if e = 2, and 0 otherwise. - Amiram Eldar, Nov 19 2021
|
|
MATHEMATICA
|
f[p_, e_] := Which[e > 2, 0, e == 2, p^2 - p, e == 1, 1 - p]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 19 2021 *)
|
|
PROG
|
(PARI)
A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); }; \\ From A057521
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|