A336468 a(n) = A336466(phi(n)), where A336466 is fully multiplicative with a(p) = A000265(p-1) for prime p, with A000265(k) giving the odd part of k.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 5, 11, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 3, 7, 1, 1, 1, 1, 1, 1, 1, 5, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 3, 3, 1, 5, 1, 1, 5, 1, 11, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Jul 22 2020

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000010, A000265, A336466, A336469.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A336468(n) = { my(f=factor(eulerphi(n))); prod(k=1,#f~,A000265(f[k,1]-1)^f[k,2]); };
\\ Alternatively, as follows, requiring also code from A336466:
A336468(n) = { my(f=factor(n)); prod(k=1,#f~,A336466(f[k,1]-1) * A336466(f[k,1])^(f[k,2]-1)); };

Formula

a(n) = A336466(A000010(n)).

Multiplicative with a(p^e) = A336466(p-1) * A336466(p)^(e-1).