A336456 a(n) = A335915(sigma(sigma(n))), where A335915 is a fully multiplicative sequence with a(2) = 1 and a(p) = A000265(p^2 - 1) for odd primes p, with A000265(k) giving the odd part of k.

1, 1, 3, 1, 1, 3, 3, 1, 3, 21, 3, 3, 1, 3, 3, 1, 21, 3, 3, 1, 3, 63, 3, 3, 1, 1, 3, 3, 1, 63, 3, 21, 15, 3, 15, 3, 3, 3, 3, 21, 1, 3, 3, 3, 3, 63, 15, 3, 3, 1, 63, 45, 3, 3, 63, 3, 15, 21, 3, 3, 1, 3, 9, 1, 3, 315, 3, 21, 3, 315, 63, 3, 45, 3, 3, 3, 3, 3, 15, 1, 135, 21, 3, 3, 9, 3, 3, 63, 21, 63, 15, 3, 27, 315

Offset: 1

Author

Antti Karttunen, Jul 22 2020

Keywords

• nonn

Comments

Like A051027, neither this is multiplicative. For example, we have a(3) = 3, a(7) = 3, but a(21) = 3 <> 9. However, for example, a(10) = 21, and a(3*10) = 63.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000203, A051027, A335915.

Cf. also A336462, A336463, A336464.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A335915(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265((f[k,1]^2)-1)^f[k,2]))); };
A336456(n) = A335915(sigma(sigma(n)));

Formula

a(n) = A335915(A000203(A000203(n))) = A336455(A000203(n)) = A335915(A051027(n)).