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

1,5

Comments

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

Links

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A329646 A293813 A381708 * A218585 A279507 A054656

Adjacent sequences: A385119 A385120 A385121 * A385123 A385124 A385125

Keyword

sign

Author

Sean A. Irvine, Jun 18 2025

Status

approved