A372380 - OEIS

A372380

The number of divisors of n that are numbers whose number of divisors is a power of 2.

1, 2, 2, 2, 2, 4, 2, 3, 2, 4, 2, 4, 2, 4, 4, 3, 2, 4, 2, 4, 4, 4, 2, 6, 2, 4, 3, 4, 2, 8, 2, 3, 4, 4, 4, 4, 2, 4, 4, 6, 2, 8, 2, 4, 4, 4, 2, 6, 2, 4, 4, 4, 2, 6, 4, 6, 4, 4, 2, 8, 2, 4, 4, 3, 4, 8, 2, 4, 4, 8, 2, 6, 2, 4, 4, 4, 4, 8, 2, 6, 3, 4, 2, 8, 4, 4, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

First differs from A061389 and A322483 at n = 32.

LINKS

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

FORMULA

Multiplicative with a(p^e) = floor(log_2(e+1)) + 1.

a(n) = A000005(n) if and only if n is squarefree (A005117).

MATHEMATICA

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