A338539 - OEIS

%I #15 Oct 12 2024 16:37:25

%S 36,72,100,108,144,180,196,200,216,225,252,288,300,324,360,392,396,

%T 400,432,441,450,468,484,500,504,540,576,588,600,612,648,675,676,684,

%U 700,720,756,784,792,800,828,864,882,936,968,972,980,1000,1008,1044,1080,1089

%N Numbers having exactly two non-unitary prime factors.

%C Numbers k such that A056170(k) = A001221(A057521(k)) = 2.

%C Numbers divisible by the squares of exactly two distinct primes.

%C Subsequence of A036785 and first differs from it at n = 44.

%C The asymptotic density of this sequence is (3/Pi^2)*(eta_1^2 - eta_2) = 0.0532928864..., where eta_j = Sum_{p prime} 1/(p^2-1)^j (Pomerance and Schinzel, 2011).

%H Amiram Eldar, <a href="/A338539/b338539.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 36 = 2^2 * 3^2 is a term since it has exactly 2 prime factors, 2 and 3, that are non-unitary.

%t Select[Range[1000], Count[FactorInteger[#][[;;,2]], _?(#1 > 1 &)] == 2 &]

%Y Subsequence of A013929 and A036785.

%Y Cf. A001221, A056170, A057521, A190641, A338540, A338541, A338542, A347892 (subsequence).

%Y Cf. A154945 (eta_1), A324833 (eta_2).

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 01 2020