A336455 a(n) = A335915(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, 1, 3, 1, 1, 1, 3, 21, 1, 1, 3, 3, 1, 1, 15, 1, 21, 3, 3, 1, 1, 1, 3, 15, 3, 3, 3, 3, 1, 1, 3, 1, 1, 1, 63, 45, 3, 3, 3, 3, 1, 15, 3, 21, 1, 1, 15, 45, 15, 1, 9, 1, 3, 1, 3, 3, 3, 3, 3, 15, 1, 21, 63, 3, 1, 9, 3, 1, 1, 1, 63, 171, 45, 15, 9, 1, 3, 3, 15, 225, 3, 3, 3, 1, 15, 3, 3, 3, 21, 3, 3, 1, 1, 3, 3, 9, 45, 21, 45

Offset: 1

Author

Antti Karttunen, Jul 22 2020

Keywords

• nonn
• mult

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. A000265, A000203, A335915, A336456.

Cf. also A336461, A336462, 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]))); };
A336455(n) = A335915(sigma(n));
\\ Alternatively, as:
A336455(n) =  { my(f=factor(n)); prod(k=1,#f~,A335915(((f[k,1]^(1+f[k,2]))-1)/(f[k,1]-1))); };

Formula

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

Multiplicative with a(p^e) = A335915(1 + p + p^2 + ... + p^e).

a(A000203(n)) = A336456(n).