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

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]

Prog

(PARI) a(n) = vecprod(apply(x -> exponent(x+1)+1, factor(n)[, 2]));
(Python)
from math import prod
from sympy import factorint
def A372380(n): return prod((e+1).bit_length() for e in factorint(n).values()) # Chai Wah Wu, Apr 30 2024

Crossrefs

Cf. A000005, A005117, A036537, A372379.

Cf. A061389, A322483.

Sequence in context: A368883 A379028 A173439 * A322483 A061389 A366763

Adjacent sequences: A372377 A372378 A372379 * A372381 A372382 A372383

Keyword

nonn,easy,mult

Author

Amiram Eldar, Apr 29 2024

Status

approved