A353647 Möbius transform of A062401, where A062401(n) = phi(sigma(n)).

1, 1, 1, 4, 1, 1, 3, 2, 10, 3, 3, 4, 5, 3, 5, 22, 5, 10, 7, 2, 11, 7, 7, 2, 28, 5, 4, 12, 7, 11, 15, 6, 11, 11, 11, 40, 17, 7, 17, 10, 11, 11, 19, 8, 6, 15, 15, 22, 32, 26, 17, 26, 17, 4, 19, 6, 23, 15, 15, 14, 29, 15, 22, 90, 17, 23, 31, 14, 23, 25, 23, 20, 35, 17, 24, 28, 25, 17, 31, 14, 94, 23, 23, 44, 29, 19

Offset: 1

Author

Antti Karttunen, May 06 2022

Keywords

• sign

Comments

The first negative term is a(1944) = -76.

Links

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

Crossrefs

Cf. A000010, A000203, A008683, A062401.

Programs

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[n/#] * EulerPhi[DivisorSigma[1, #]] &]; Array[a, 100] (* Amiram Eldar, May 06 2022 *)

PARI

A353647(n) = sumdiv(n,d,moebius(n/d)*eulerphi(sigma(d)));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A062401(d).