A353753 a(n) = phi(sigma(n)) - Product_{p^e||n} phi(sigma(p^e)), where n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 8, 6, 8, 0, 0, 0, 12, 8, 0, 16, 0, 0, 0, 8, 0, 0, 0, 0, 12, 6, 0, 0, 16, 0, 16, 8, 0, 24, 0, 0, 0, 0, 12, 32, 0, 0, 16, 32, 0, 0, 0, 0, 0, 0, 16, 24, 0, 0, 0, 12, 0, 48, 24, 0, 16, 16, 0, 24, 24, 0, 32, 16, 16, 0, 0, 36

Offset: 1

Author

Antti Karttunen, May 08 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A000010, A000203, A062401, A353752, A353754, A353755.

Cf. A336547 (positions of 0's), A336548 (positions of terms > 0).

Cf. also A353803.

Programs

PARI

A062401(n) = eulerphi(sigma(n));
A353753(n) = { my(f = factor(n)); A062401(n)-prod(k=1, #f~, A062401(f[k, 1]^f[k, 2])); };

Formula

a(n) = A062401(n) - A353752(n).