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

1,1

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).

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.

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 &]

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).

Sequence in context: A344694 A127658 A318720 * A137490 A129575 A328136

Adjacent sequences: A338537 A338538 A338539 * A338541 A338542 A338543

Keyword

nonn

Author

Amiram Eldar, Nov 01 2020

Status

approved