A324391 Fully multiplicative with a(p^e) = A070939(p)^e, where A070939(p) gives the length of the binary representation of p.

1, 2, 2, 4, 3, 4, 3, 8, 4, 6, 4, 8, 4, 6, 6, 16, 5, 8, 5, 12, 6, 8, 5, 16, 9, 8, 8, 12, 5, 12, 5, 32, 8, 10, 9, 16, 6, 10, 8, 24, 6, 12, 6, 16, 12, 10, 6, 32, 9, 18, 10, 16, 6, 16, 12, 24, 10, 10, 6, 24, 6, 10, 12, 64, 12, 16, 7, 20, 10, 18, 7, 32, 7, 12, 18, 20, 12, 16, 7, 48, 16, 12, 7, 24, 15, 12, 10, 32, 7, 24, 12, 20, 10, 12

Offset: 1

Author

Antti Karttunen, Mar 05 2019

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000043, A000668, A070939, A072084.

Programs

PARI

A070939(n) = if(!n,1,#binary(n));
A324391(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = A070939(f[i, 1])); factorback(f); };

Formula

For all n >= 1, a(A000668(n)) = A000043(n).