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