cp's OEIS Frontend

A372381 The number of divisors of the largest divisor of n whose number of divisors is a power of 2.

%I A372381 #13 Apr 30 2024 11:43:48
%S A372381 1,2,2,2,2,4,2,4,2,4,2,4,2,4,4,4,2,4,2,4,4,4,2,8,2,4,4,4,2,8,2,4,4,4,
%T A372381 4,4,2,4,4,8,2,8,2,4,4,4,2,8,2,4,4,4,2,8,4,8,4,4,2,8,2,4,4,4,4,8,2,4,
%U A372381 4,8,2,8,2,4,4,4,4,8,2,8,4,4,2,8,4,4,4
%N A372381 The number of divisors of the largest divisor of n whose number of divisors is a power of 2.
%C A372381 First differs from A286324 at n = 32, and from A331109 at n = 64.
%C A372381 Also, the number of infinitary divisors of the largest divisor of n whose number of divisors is a power of 2.
%H A372381 Amiram Eldar, <a href="/A372381/b372381.txt">Table of n, a(n) for n = 1..10000</a>
%F A372381 Multiplicative with a(p^e) = 2^floor(log_2(e+1)).
%F A372381 a(n) = A000005(A372379(n)).
%F A372381 a(n) = A037445(A372379(n)).
%F A372381 a(n) = A000005(n) if and only if n is in A036537.
%F A372381 a(n) <= A372380(n), with equality if and only if n is cubefree (A004709).
%t A372381 f[p_, e_] := 2^Floor[Log2[e + 1]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A372381 (PARI) a(n) = vecprod(apply(x -> 2^exponent(x+1), factor(n)[, 2]));
%o A372381 (Python)
%o A372381 from math import prod
%o A372381 from sympy import factorint
%o A372381 def A372381(n): return prod(1<<(e+1).bit_length()-1 for e in factorint(n).values()) # _Chai Wah Wu_, Apr 30 2024
%Y A372381 Cf. A000005, A004709, A036537, A037445, A372379, A372380.
%Y A372381 Cf. A286324, A331109.
%K A372381 nonn,easy,mult
%O A372381 1,2
%A A372381 _Amiram Eldar_, Apr 29 2024