A353806 a(n) = A353802(n) / gcd(A051027(n), A353802(n)), where A051027(n) = sigma(sigma(n)), and A353802(n) = Product_{p^e||n} sigma(sigma(p^e)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 5, 16, 1, 1, 1, 1, 1, 1, 1, 112, 1, 1, 49, 13, 45, 1, 1, 1, 7, 16, 1, 5, 1, 1, 1, 16, 1, 1, 1, 1, 7, 64, 1, 1, 112, 1, 49, 16, 1, 7, 1, 1, 1, 1, 9, 784, 1, 1, 5, 720, 1, 1, 1, 1, 1, 1, 5, 7, 1, 1, 1, 16, 1, 5, 117, 1, 7, 16, 1, 16, 45, 1, 147, 16, 7

Offset: 1

Author

Antti Karttunen, May 08 2022

Keywords

• nonn
• frac

Comments

Numerator of fraction A353802(n) / A051027(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A051027, A353802, A353803, A353804, A353805 (denominators).

Cf. A336547 (positions of 1's), A336548 (positions of terms > 1), see also A353807.

Cf. also A353755, A353756.

Programs

PARI

A051027(n) = sigma(sigma(n));
A353806(n) = { my(f = factor(n), u=prod(k=1, #f~, A051027(f[k, 1]^f[k, 2]))); (u / gcd(A051027(n), u)); };

Formula

a(n) = A353802(n) / A353804(n) = A353802(n) / gcd(A051027(n), A353802(n)).