A338539 Numbers having exactly two non-unitary prime factors.

36, 72, 100, 108, 144, 180, 196, 200, 216, 225, 252, 288, 300, 324, 360, 392, 396, 400, 432, 441, 450, 468, 484, 500, 504, 540, 576, 588, 600, 612, 648, 675, 676, 684, 700, 720, 756, 784, 792, 800, 828, 864, 882, 936, 968, 972, 980, 1000, 1008, 1044, 1080, 1089

Offset: 1

Author

Amiram Eldar, Nov 01 2020

Keywords

• nonn

Comments

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

Numbers divisible by the squares of exactly two distinct primes.

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

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).

Examples

			36 = 2^2 * 3^2 is a term since it has exactly 2 prime factors, 2 and 3, that are non-unitary.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Carl Pomerance and Andrzej Schinzel, Multiplicative Properties of Sets of Residues, Moscow Journal of Combinatorics and Number Theory, Vol. 1, No. 1 (2011), pp. 52-66. See pp. 61-62.

Crossrefs

Subsequence of A013929 and A036785.

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

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

Programs

Mathematica

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