A353636 Difference between phi(sigma(n)) and phi(n).

0, 1, 0, 4, -2, 2, -2, 4, 6, 2, -6, 8, -6, 2, 0, 22, -10, 18, -10, 4, 4, 2, -14, 8, 10, 0, -2, 12, -20, 16, -14, 20, -4, 2, -8, 60, -18, -2, 0, 8, -28, 20, -22, 4, 0, 2, -30, 44, -6, 40, -8, 18, -34, 14, -16, 8, -4, -4, -42, 32, -30, 2, 12, 94, -24, 28, -34, 4, -12, 24, -46, 72, -36, 0, 20, 12, -28, 24, -46, 28, 56

Offset: 1

Author

Antti Karttunen, May 04 2022

Keywords

• sign
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000010, A000203, A007431, A062401, A353643, A353647.

Cf. A006872 (positions of zeros), A353637 (their characteristic function).

Cf. A353682 (positions of terms >= 0), A353683 (of terms > 0), A353685 (of terms <= 0), A353686 (of negative terms).

Cf. also A351445.

Programs

Mathematica

a[n_] := EulerPhi[DivisorSigma[1, n]] - EulerPhi[n]; Array[a, 100] (* Amiram Eldar, May 06 2022 *)

PARI

A353636(n) = (eulerphi(sigma(n))-eulerphi(n));

Formula

a(n) = A062401(n) - A000010(n) = A000010(A000203(n)) - A000010(n).

a(n) = Sum_{d|n} (A353647(d) - A007431(d)).