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%I #10 Nov 02 2020 02:00:20
%S 44100,88200,108900,132300,152100,176400,213444,217800,220500,260100,
%T 264600,298116,304200,308700,324900,326700,352800,396900,426888,
%U 435600,441000,456300,476100,485100,509796,520200,529200,544500,573300,592900,596232,608400,617400
%N Numbers having exactly four non-unitary prime factors.
%C Numbers k such that A056170(k) = A001221(A057521(k)) = 4.
%C Numbers divisible by the squares of exactly four distinct primes.
%C The asymptotic density of this sequence is (eta_1^4 - 6*eta_1^2*eta_2 + 3*eta_2^2 + 8*eta_1*eta_3 - 6*eta_4)/(4*Pi^2) = 0.0000970457..., where eta_j = Sum_{p prime} 1/(p^2-1)^j (Pomerance and Schinzel, 2011).
%H Amiram Eldar, <a href="/A338541/b338541.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 44100 = 2^2 * 3^2 * 5^2 * 7^2 is a term since it has exactly 4 prime factors, 2, 3, 5 and 7, that are non-unitary.
%t Select[Range[620000], Count[FactorInteger[#][[;;,2]], _?(#1 > 1 &)] == 4 &]
%Y Subsequence of A013929 and A318720.
%Y Cf. A001221, A056170, A057521, A190641, A338539, A338540, A338542.
%Y Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3), A324835 (eta_4).
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 01 2020
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