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A381576 a(n) is the second element of the sorted multiset of bases and exponents (including exponents = 1) in the prime factorization of n.

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%I A381576 #6 Mar 01 2025 12:19:45
%S A381576 2,3,2,5,1,7,3,3,1,11,2,13,1,1,4,17,2,19,2,1,1,23,2,5,1,3,2,29,1,31,5,
%T A381576 1,1,1,2,37,1,1,2,41,1,43,2,2,1,47,2,7,2,1,2,53,2,1,2,1,1,59,1,61,1,2,
%U A381576 6,1,1,67,2,1,1,71,2,73,1,2,2,1,1,79,2,4,1,83,1,1,1
%N A381576 a(n) is the second element of the sorted multiset of bases and exponents (including exponents = 1) in the prime factorization of n.
%H A381576 Paolo Xausa, <a href="/A381576/b381576.txt">Table of n, a(n) for n = 2..10000</a>
%F A381576 a(p) = p, for p prime.
%e A381576 a(10) = 1 because the prime factorization of 10 is 2^1*5^1, the multiset of these bases and exponents is {1, 1, 2, 5} and its second element is 1.
%e A381576 a(18) = 2 because the prime factorization of 18 is 2^1*3^2, the multiset of these bases and exponents is {1, 2, 2, 3} and its second element is 2.
%t A381576 A381576[n_] := Sort[Flatten[FactorInteger[n]]][[2]];
%t A381576 Array[A381576, 100, 2]
%Y A381576 Second column of A381178.
%K A381576 nonn,easy
%O A381576 2,1
%A A381576 _Paolo Xausa_, Feb 28 2025