A338540 Numbers having exactly three non-unitary prime factors.

900, 1764, 1800, 2700, 3528, 3600, 4356, 4500, 4900, 5292, 5400, 6084, 6300, 7056, 7200, 8100, 8712, 8820, 9000, 9800, 9900, 10404, 10584, 10800, 11025, 11700, 12100, 12168, 12348, 12600, 12996, 13068, 13500, 14112, 14400, 14700, 15300, 15876, 16200, 16900, 17100

Offset: 1

Author

Amiram Eldar, Nov 01 2020

Keywords

• nonn

Comments

Numbers k such that A056170(k) = A001221(A057521(k)) = 3.

Numbers divisible by the squares of exactly three distinct primes.

Subsequence of A318720 and first differs from it at n = 123.

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).

Examples

			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.
		

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, A318720 and A327877.

Cf. A001221, A056170, A057521, A190641, A338539, A338541, A338542.

Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3).

Programs

Mathematica

Select[Range[17000], Count[FactorInteger[#][[;;,2]], _?(#1 > 1 &)] == 3 &]