A303809 Multiplicative with a(p^k) = 2^a(k).

1, 2, 2, 4, 2, 4, 2, 4, 4, 4, 2, 8, 2, 4, 4, 16, 2, 8, 2, 8, 4, 4, 2, 8, 4, 4, 4, 8, 2, 8, 2, 4, 4, 4, 4, 16, 2, 4, 4, 8, 2, 8, 2, 8, 8, 4, 2, 32, 4, 8, 4, 8, 2, 8, 4, 8, 4, 4, 2, 16, 2, 4, 8, 16, 4, 8, 2, 8, 4, 8, 2, 16, 2, 4, 8, 8, 4, 8, 2, 32, 16, 4, 2, 16

Offset: 1

Author

Rémy Sigrist, Apr 30 2018

Keywords

• nonn
• easy
• mult

Comments

This sequence contains every power of 2; see A303819 for the corresponding least indices.

For any n > 0, a(n) only depends on the prime signature of n.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A014221, A061142, A303819.

Programs

PARI

a(n) = my (f=factor(n)); prod (i=1, #f~, 2^a(f[i, 2]))

Formula

a(n) <= n with equality iff n = A014221(k) for some k >= 0.

a(A002110(k)) = 2^k for any k >= 0.

a(n) = 2 iff n is prime.