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A333634 Numbers with an even number of non-unitary prime divisors.

%I A333634 #53 Jul 14 2020 03:36:35
%S A333634 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,30,31,33,34,35,36,37,
%T A333634 38,39,41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,70,71,72,73,
%U A333634 74,77,78,79,82,83,85,86,87,89,91,93,94,95,97,100,101,102
%N A333634 Numbers with an even number of non-unitary prime divisors.
%C A333634 Numbers that have an even number of distinct prime factors raised to a power larger than 1.
%C A333634 The asymptotic density of this sequence is 0.661317... (A065493, Feller and Tornier, 1933).
%H A333634 Amiram Eldar, <a href="/A333634/b333634.txt">Table of n, a(n) for n = 1..10000</a>
%H A333634 Willy Feller and Erhard Tornier, <a href="https://doi.org/10.1007/BF01448890">Mengentheoretische Untersuchung von Eigenschaften der Zahlenreihe</a>, Mathematische Annalen, Vol. 107 (1933), pp. 188-232.
%H A333634 I. J. Schoenberg, <a href="https://doi.org/10.1090/S0002-9947-1936-1501849-X">On asymptotic distributions of arithmetical functions</a>, Transactions of the American Mathematical Society, Vol. 39, No. 2 (1936), pp. 315-330. See p. 326.
%H A333634 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Feller-TornierConstant.html">Feller-Tornier Constant</a>.
%H A333634 Wikipedia, <a href="https://en.wikipedia.org/wiki/Feller%E2%80%93Tornier_constant">Feller-Tornier constant</a>.
%F A333634 Numbers k with A056170(k) == 0 (mod 2).
%e A333634 1 is a term since it has 0 prime divisors, and 0 is even.
%e A333634 180 is a term since 180 = 2^2 * 3^2 * 5 has 2 prime divisors, 2 and 3, with exponents larger than 1 in its prime factorization, and 2 is even.
%t A333634 Select[Range[100], EvenQ @ Count[FactorInteger[#][[;;,2]], u_ /; u > 1]  &]
%Y A333634 Cf. A056170, A065493, A190641, A327877 (complement).
%K A333634 nonn
%O A333634 1,2
%A A333634 _Amiram Eldar_, May 23 2020