A336459 a(n) = A065330(sigma(sigma(n))), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.

1, 1, 7, 1, 1, 7, 5, 1, 7, 13, 7, 7, 1, 5, 5, 1, 13, 7, 7, 1, 7, 91, 5, 7, 1, 1, 5, 5, 1, 65, 7, 13, 31, 5, 31, 7, 5, 7, 5, 13, 1, 7, 7, 7, 7, 65, 31, 7, 5, 1, 65, 19, 5, 5, 65, 5, 31, 13, 7, 5, 1, 7, 35, 1, 7, 403, 7, 13, 7, 403, 65, 7, 19, 5, 7, 7, 7, 5, 31, 1, 133, 13, 7, 7, 35, 7, 5, 91, 13, 91, 31, 5, 85, 403

Offset: 1

Author

Antti Karttunen, Jul 25 2020

Keywords

• nonn

Comments

Sequence removes prime factors 2 and 3 from the prime factorization A051027(n) = sigma(sigma(n)).

Like A051027, neither this is multiplicative. For example, we have a(3) = 7, a(7) = 5, but a(21) = 7 <> 35. However, for example, a(10) = 13, and a(3*10) = a(3)*a(10) = 65.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A051027, A065330, A336456 (similar sequence), A336457.

Cf. also A336561 (positions where this appears to be multiplicative but A051027 does not).

Programs

PARI

A065330(n) = (n>>valuation(n, 2)/3^valuation(n, 3));
A336459(n) = A065330(sigma(sigma(n)));

Formula

a(n) = A336457(A000203(n)) = A065330(A051027(n)).