A179115 a(n) = Sum_{d|n} phi(d^tau(d)).

1, 3, 7, 35, 21, 441, 43, 2083, 493, 4023, 111, 995801, 157, 16509, 27027, 526371, 273, 11338335, 343, 25604055, 111181, 106593, 507, 36692769241, 12521, 211071, 354787, 206540957, 813, 174960031461, 931, 537397283, 718857, 629139, 1029063, 33853331223167, 1333

Offset

1,2

Comments

Inverse Möbius transform of phi(n^tau(n)). - Wesley Ivan Hurt, Jun 09 2023

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

Equals the logarithmic derivative of A179114.

a(n) = Sum_{k=1..n} phi(gcd(n,k)^tau(gcd(n,k)))/phi(n/gcd(n,k)). - Richard L. Ollerton, May 09 2021

Maple

a:= proc(n) uses numtheory; add(phi(d^tau(d)), d=divisors(n)) end:
seq(a(n), n=1..40);  # Alois P. Heinz, Sep 21 2024

Mathematica

a[n_] := Sum[EulerPhi[d^DivisorSigma[0, d]], {d, Divisors[n]}];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 23 2025 *)

Prog

(PARI) {a(n)=sumdiv(n, d, eulerphi(d^sigma(d, 0)))}

Crossrefs

Cf. A179114, A000010 (phi), A000005 (tau).

Sequence in context: A365140 A318444 A334314 * A299300 A047907 A328420

Adjacent sequences: A179112 A179113 A179114 * A179116 A179117 A179118

Keyword

nonn

Author

Paul D. Hanna, Jul 10 2010

Extensions

Offset changed to 1 by Georg Fischer, Sep 21 2024

Status

approved