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A372380
The number of divisors of n that are numbers whose number of divisors is a power of 2.
3
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
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
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Apr 29 2024
STATUS
approved