A078150 -id:A078150 - cp's OEIS frontend

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

Sean A. Irvine, Jun 18 2025

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

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

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

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

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

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

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

A078151 Smallest k such that d(phi(k)) - phi(d(k)) = -n, where d(k) = A000005(k) and phi(k) = A000010(k).

Original entry on oeis.org

240, 120, 960, 6528, 4080, 1920, 15360, 24960, 61440, 13440, 16320, 87360, 983040, 196560, 1432080, 130560, 861840, 32640, 98280, 114240, 2545920, 293760, 261120, 967680, 174720, 2673216, 4194240, 1081080, 1044480, 913920, 1659840, 424320

Offset: 1

Labos Elemer, Nov 26 2002

			a(77)=2970240, since d(phi(2970240)) - phi(d(2970240)) = -77 first appears here; while d(phi(x)) - phi(d(x)) takes large positive values,absolute value of negative differences grows significantly slower.

Cf. A000005, A000010, A078150.

Least inverse of -A385122.

cp's OEIS Frontend

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.

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A078151 Smallest k such that d(phi(k)) - phi(d(k)) = -n, where d(k) = A000005(k) and phi(k) = A000010(k).

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