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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to sigma(n)

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).

Prog

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

Crossrefs

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

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

Cf. also A353802.

Sequence in context: A124859 A021446 A353754 * A062401 A286383 A138949

Adjacent sequences: A353749 A353750 A353751 * A353753 A353754 A353755

Keyword

nonn,mult

Author

Antti Karttunen, May 08 2022

Status

approved