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

1,10

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to sigma(n)

Formula

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

Prog

(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])); };

Crossrefs

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

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

Cf. also A353803.

Sequence in context: A083804 A341840 A028597 * A028617 A261470 A006792

Adjacent sequences: A353750 A353751 A353752 * A353754 A353755 A353756

Keyword

nonn

Author

Antti Karttunen, May 08 2022

Status

approved