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A381399 a(n) is the number of prime elements in the set of bases and exponents in the prime factorization of n.

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%I A381399 #9 Feb 25 2025 11:39:39
%S A381399 0,1,1,1,1,2,1,2,2,2,1,2,1,2,2,1,1,2,1,2,2,2,1,2,2,2,1,2,1,3,1,2,2,2,
%T A381399 2,2,1,2,2,3,1,3,1,2,3,2,1,2,2,2,2,2,1,2,2,3,2,2,1,3,1,2,3,1,2,3,1,2,
%U A381399 2,3,1,2,1,2,3,2,2,3,1,2,1,2,1,3,2,2,2,3,1,3
%N A381399 a(n) is the number of prime elements in the set of bases and exponents in the prime factorization of n.
%C A381399 Differs from A115588 at n = 64, 81, 256, 320, 405, 448, 512... =  A381400.
%H A381399 Paolo Xausa, <a href="/A381399/b381399.txt">Table of n, a(n) for n = 1..10000</a>
%e A381399 a(144) = 2 because the prime factorization of 144 is 2^4*3^2 and the set of these bases and exponents is {2, 3, 4}, containing 2 primes.
%t A381399 A381399[n_] := Count[Union[Flatten[FactorInteger[n]]], _?PrimeQ];
%t A381399 Array[A381399, 100]
%Y A381399 Cf. A115588, A381398, A381400, A381401.
%K A381399 nonn,easy
%O A381399 1,6
%A A381399 _Paolo Xausa_, Feb 22 2025