A353754 Greatest common divisor of phi(sigma(n)) and 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.

1, 2, 2, 6, 2, 4, 4, 8, 12, 2, 4, 12, 6, 8, 4, 30, 6, 24, 8, 12, 8, 4, 8, 16, 30, 12, 16, 24, 8, 8, 16, 36, 8, 6, 8, 72, 18, 16, 12, 8, 12, 16, 20, 24, 24, 8, 16, 60, 36, 60, 12, 6, 18, 32, 8, 32, 16, 8, 16, 24, 30, 32, 48, 126, 12, 16, 32, 36, 16, 16, 24, 96, 36, 36, 60, 48, 16, 24, 32, 60, 110, 12, 24, 48, 12, 40

Offset: 1

Author

Antti Karttunen, May 08 2022

Keywords

• nonn

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, A353752, A353753, A353755, A353756.

Cf. also A353804.

Programs

PARI

A062401(n) = eulerphi(sigma(n));
A353754(n) = { my(f = factor(n)); gcd(A062401(n), prod(k=1, #f~, A062401(f[k, 1]^f[k, 2]))); };

Formula

a(n) = gcd(A062401(n), A353752(n)) = gcd(A062401(n), A353753(n)) = gcd(A353752(n), A353753(n)).

a(n) = A062401(n) / A353755(n) = A353752(n) / A353756(n).