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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
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
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. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3).
Sequence in context: A344694 A127658 A318720 * A137490 A129575 A328136
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 01 2020
STATUS
approved