A385122 a(n) = d(phi(n)) - phi(d(n)) where d(n) = A000005(n) is the number of divisors and phi(n) = A000010(n) is the Euler totient function.

0, 0, 1, 0, 2, 0, 3, 1, 2, 1, 3, 1, 5, 2, 2, 0, 4, 2, 5, 2, 4, 2, 3, 0, 4, 4, 4, 4, 5, 0, 7, 3, 4, 3, 6, 0, 8, 4, 6, 1, 7, 2, 7, 4, 6, 2, 3, 1, 6, 4, 4, 6, 5, 2, 6, 4, 7, 4, 3, 1, 11, 6, 7, 0, 8, 2, 7, 4, 4, 4, 7, 4, 11, 7, 6, 7, 10, 4, 7, 2, 4, 6, 3, 4, 5, 6

Offset: 1

Author

Sean A. Irvine, Jun 18 2025

Keywords

• sign

Comments

First negative value is a(120) = -2.

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000010, A062821, A078148, A078150, A163109.

Programs

Mathematica

A385122[n_] := DivisorSigma[0, EulerPhi[n]] - EulerPhi[DivisorSigma[0, n]];
Array[A385122, 100] (* Paolo Xausa, Jun 19 2025 *)

PARI

a(n) = numdiv(eulerphi(n)) - eulerphi(numdiv(n)); \\ Michel Marcus, Jun 19 2025

Formula

a(n) = A000005(A000010(n)) - A000010(A000005(n)).

a(n) = A062821(n) - A163109(n).