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A348097 Numbers having equally many unitary and nonunitary prime divisors.

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%I A348097 #14 Sep 30 2021 17:32:37
%S A348097 1,12,18,20,24,28,40,44,45,48,50,52,54,56,63,68,75,76,80,88,92,96,98,
%T A348097 99,104,112,116,117,124,135,136,147,148,152,153,160,162,164,171,172,
%U A348097 175,176,184,188,189,192,207,208,212,224,232,236,242,244,245,248,250,261
%N A348097 Numbers having equally many unitary and nonunitary prime divisors.
%C A348097 A prime divisor of k is unitary if its exponent in the prime factorization of k is 1, and is nonunitary otherwise.
%C A348097 Numbers k such that A056169(k) = A056170(k) = A001221(k)/2.
%C A348097 A345381 is a subsequence. After a(1) = 1, a(238) = 1260 is the next term that is not in A345381.
%H A348097 Amiram Eldar, <a href="/A348097/b348097.txt">Table of n, a(n) for n = 1..10000</a>
%e A348097 12 = 2^2 * 3 is a term since it has one unitary prime divisor (3) and one nonunitary prime divisor (2).
%t A348097 q[n_] := n == 1 || Count[(e = FactorInteger[n][[;; , 2]]), 1] == Length[e]/2; Select[Range[300], q]
%Y A348097 Cf. A001221, A056169, A056170, A345381.
%Y A348097 Subsequence of A030231.
%Y A348097 Similar sequences: A016825 (odd and even divisors), A048109, A187039.
%K A348097 nonn
%O A348097 1,2
%A A348097 _Amiram Eldar_, Sep 30 2021