A353898 a(n) is the number of divisors of n whose exponents in their prime factorizations are all powers of 2 (A138302).

1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 4, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 3, 6, 2, 8, 2, 4, 4, 4, 4, 9, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 8, 3, 6, 4, 6, 2, 6, 4, 6, 4, 4, 2, 12, 2, 4, 6, 4, 4, 8, 2, 6, 4, 8, 2, 9, 2, 4, 6, 6, 4, 8, 2, 8, 4, 4, 2, 12, 4, 4, 4

Offset: 1

Author

Amiram Eldar, May 10 2022

Keywords

• nonn
• mult

Comments

First differs from A049599 and A282446 at n=32.

Examples

			The divisors of 8 are 1, 2 = 2^1, 4 = 2^2 and 8 = 2^3. 3 of these divisors, 1, 2 and 4, are in A138302. Therefore, a(8) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A004709, A049599, A138302, A282446, A353897.

Similar sequences: A034444, A048105, A286324, A049419.

Programs

Mathematica

f[p_, e_] := Floor[Log2[e]] + 2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Formula

Multiplicative with a(p^e) = floor(log_2(e)) + 2.

a(n) > 1 for n > 1 and a(n) = 2 if and only if n is a prime.

a(n) = A000005(n) if and only if n is cubefree (A004709).