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A338539
Numbers having exactly two non-unitary prime factors.
8
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
1,1
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).
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
36 = 2^2 * 3^2 is a term since it has exactly 2 prime factors, 2 and 3, that are non-unitary.
MATHEMATICA
Select[Range[1000], Count[FactorInteger[#][[;; , 2]], _?(#1 > 1 &)] == 2 &]
CROSSREFS
Subsequence of A013929 and A036785.
Cf. A154945 (eta_1), A324833 (eta_2).
Sequence in context: A335463 A192026 A036785 * A347960 A286708 A355462
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 01 2020
STATUS
approved