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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A372380 The number of divisors of n that are numbers whose number of divisors is a power of 2.

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%I A372380 #15 Apr 22 2025 08:58:36
%S A372380 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,
%T A372380 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,
%U A372380 4,8,2,6,2,4,4,4,4,8,2,6,3,4,2,8,4,4,4
%N A372380 The number of divisors of n that are numbers whose number of divisors is a power of 2.
%C A372380 First differs from A061389 and A322483 at n = 32.
%C A372380 First differs from A380922 at n = 128. - _Vaclav Kotesovec_, Apr 22 2025
%H A372380 Amiram Eldar, <a href="/A372380/b372380.txt">Table of n, a(n) for n = 1..10000</a>
%F A372380 Multiplicative with a(p^e) = floor(log_2(e+1)) + 1.
%F A372380 a(n) = A000005(n) if and only if n is squarefree (A005117).
%t A372380 f[p_, e_] := Floor[Log2[e + 1]] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A372380 (PARI) a(n) = vecprod(apply(x -> exponent(x+1)+1, factor(n)[, 2]));
%o A372380 (Python)
%o A372380 from math import prod
%o A372380 from sympy import factorint
%o A372380 def A372380(n): return prod((e+1).bit_length() for e in factorint(n).values()) # _Chai Wah Wu_, Apr 30 2024
%Y A372380 Cf. A000005, A005117, A036537, A372379.
%Y A372380 Cf. A061389, A322483, A380922.
%K A372380 nonn,easy,mult
%O A372380 1,2
%A A372380 _Amiram Eldar_, Apr 29 2024