OFFSET
1,3
COMMENTS
Möbius transform of tau(n)*phi(n) (A062355).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
N. J. A. Sloane, Transforms
FORMULA
Multiplicative with a(p) = 2*p - 3 and a(p^e) = (e*p + p - e)*(p - 1)*p^(e - 2) for e > 1. - Amiram Eldar, May 16 2023
MATHEMATICA
f[p_, e_] := If[e == 1, 2*p - 3, (e*p + p - e)*(p - 1)*p^(e - 2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 16 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, numdiv(d)*eulerphi(d)*moebius(n/d)); \\ Michel Marcus, May 13 2023
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Wesley Ivan Hurt, May 12 2023
STATUS
approved