A353752 Multiplicative with a(p^e) = phi(sigma(p^e)).

1, 2, 2, 6, 2, 4, 4, 8, 12, 4, 4, 12, 6, 8, 4, 30, 6, 24, 8, 12, 8, 8, 8, 16, 30, 12, 16, 24, 8, 8, 16, 36, 8, 12, 8, 72, 18, 16, 12, 16, 12, 16, 20, 24, 24, 16, 16, 60, 36, 60, 12, 36, 18, 32, 8, 32, 16, 16, 16, 24, 30, 32, 48, 126, 12, 16, 32, 36, 16, 16, 24, 96, 36, 36, 60, 48, 16, 24, 32, 60, 110, 24, 24, 48, 12

Offset: 1

Author

Antti Karttunen, May 08 2022

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000010, A000203, A062401, A353753, A353754, A353755.

Cf. A336547 (positions where equal to A062401), A336548 (positions where less).

Cf. also A353802.

Programs

PARI

A062401(n) = eulerphi(sigma(n));
A353752(n) = { my(f = factor(n)); prod(k=1, #f~, A062401(f[k, 1]^f[k, 2])); };

Formula

Multiplicative with a(p^e) = A062401(p^e).

a(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.

a(n) = A062401(n) - A353753(n).