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

1,2

Links

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

Formula

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

Prog

(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); };

Crossrefs

Cf. A000043, A000668, A070939, A072084.

Sequence in context: A083742 A107331 A283187 * A357978 A087808 A217754

Adjacent sequences: A324388 A324389 A324390 * A324392 A324393 A324394

Keyword

nonn,mult

Author

Antti Karttunen, Mar 05 2019

Status

approved