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%I #11 Nov 02 2020 02:00:24
%S 900,1764,1800,2700,3528,3600,4356,4500,4900,5292,5400,6084,6300,7056,
%T 7200,8100,8712,8820,9000,9800,9900,10404,10584,10800,11025,11700,
%U 12100,12168,12348,12600,12996,13068,13500,14112,14400,14700,15300,15876,16200,16900,17100
%N Numbers having exactly three non-unitary prime factors.
%C Numbers k such that A056170(k) = A001221(A057521(k)) = 3.
%C Numbers divisible by the squares of exactly three distinct primes.
%C Subsequence of A318720 and first differs from it at n = 123.
%C The asymptotic density of this sequence is (eta_1^3 - 3*eta_1*eta_2 + 2*eta_3)/Pi^2 = 0.0032920755..., where eta_j = Sum_{p prime} 1/(p^2-1)^j (Pomerance and Schinzel, 2011).
%H Amiram Eldar, <a href="/A338540/b338540.txt">Table of n, a(n) for n = 1..10000</a>
%H Carl Pomerance and Andrzej Schinzel, <a href="http://mjcnt.phystech.edu/en/article.php?id=4">Multiplicative Properties of Sets of Residues</a>, Moscow Journal of Combinatorics and Number Theory, Vol. 1, No. 1 (2011), pp. 52-66. See pp. 61-62.
%e 900 = 2^2 * 3^2 * 5^2 is a term since it has exactly 3 prime factors, 2, 3 and 5, that are non-unitary.
%t Select[Range[17000], Count[FactorInteger[#][[;;,2]], _?(#1 > 1 &)] == 3 &]
%Y Subsequence of A013929, A318720 and A327877.
%Y Cf. A001221, A056170, A057521, A190641, A338539, A338541, A338542.
%Y Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3).
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 01 2020