A338540 - OEIS (original) (raw)

A338540

Numbers having exactly three non-unitary prime factors.

4

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

COMMENTS

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).

EXAMPLE

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.

MATHEMATICA

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