A322581 Sum of A003958 and its Dirichlet inverse: a(n) = A003958(n) + A097945(n).

2, 0, 0, 1, 0, 4, 0, 1, 4, 8, 0, 2, 0, 12, 16, 1, 0, 4, 0, 4, 24, 20, 0, 2, 16, 24, 8, 6, 0, 0, 0, 1, 40, 32, 48, 4, 0, 36, 48, 4, 0, 0, 0, 10, 16, 44, 0, 2, 36, 16, 64, 12, 0, 8, 80, 6, 72, 56, 0, 8, 0, 60, 24, 1, 96, 0, 0, 16, 88, 0, 0, 4, 0, 72, 32, 18, 120, 0, 0, 4, 16, 80, 0, 12, 128, 84, 112, 10, 0, 16, 144, 22, 120, 92, 144

Offset: 1

Author

Antti Karttunen, Dec 17 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A003958, A097945, A322582.

Cf. also A319340.

Programs

Mathematica

a[1] = 2; a[n_] := Times @@ ((First[#] - 1)^Last[#] & /@ FactorInteger[n]) + MoebiusMu[n] * EulerPhi[n]; Array[a, 60] (* Amiram Eldar, Dec 17 2018 *)

PARI

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A097945(n) = (moebius(n)*eulerphi(n));
A322581(n) = (A003958(n)+A097945(n));

Formula

a(n) = A003958(n) + A097945(n).