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A353898 a(n) is the number of divisors of n whose exponents in their prime factorizations are all powers of 2 (A138302).

%I A353898 #9 May 10 2022 14:24:16
%S A353898 1,2,2,3,2,4,2,3,3,4,2,6,2,4,4,4,2,6,2,6,4,4,2,6,3,4,3,6,2,8,2,4,4,4,
%T A353898 4,9,2,4,4,6,2,8,2,6,6,4,2,8,3,6,4,6,2,6,4,6,4,4,2,12,2,4,6,4,4,8,2,6,
%U A353898 4,8,2,9,2,4,6,6,4,8,2,8,4,4,2,12,4,4,4
%N A353898 a(n) is the number of divisors of n whose exponents in their prime factorizations are all powers of 2 (A138302).
%C A353898 First differs from A049599 and A282446 at n=32.
%H A353898 Amiram Eldar, <a href="/A353898/b353898.txt">Table of n, a(n) for n = 1..10000</a>
%F A353898 Multiplicative with a(p^e) = floor(log_2(e)) + 2.
%F A353898 a(n) > 1 for n > 1 and a(n) = 2 if and only if n is a prime.
%F A353898 a(n) = A000005(n) if and only if n is cubefree (A004709).
%e A353898 The divisors of 8 are 1, 2 = 2^1, 4 = 2^2 and 8 = 2^3. 3 of these divisors, 1, 2 and 4, are in A138302. Therefore, a(8) = 3.
%t A353898 f[p_, e_] := Floor[Log2[e]] + 2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%Y A353898 Cf. A000005, A004709, A049599, A138302, A282446, A353897.
%Y A353898 Similar sequences: A034444, A048105, A286324, A049419.
%K A353898 nonn,mult
%O A353898 1,2
%A A353898 _Amiram Eldar_, May 10 2022