Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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