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A338541
Numbers having exactly four non-unitary prime factors.
4
44100, 88200, 108900, 132300, 152100, 176400, 213444, 217800, 220500, 260100, 264600, 298116, 304200, 308700, 324900, 326700, 352800, 396900, 426888, 435600, 441000, 456300, 476100, 485100, 509796, 520200, 529200, 544500, 573300, 592900, 596232, 608400, 617400
OFFSET
1,1
COMMENTS
Numbers k such that A056170(k) = A001221(A057521(k)) = 4.
Numbers divisible by the squares of exactly four distinct primes.
The asymptotic density of this sequence is (eta_1^4 - 6*eta_1^2*eta_2 + 3*eta_2^2 + 8*eta_1*eta_3 - 6*eta_4)/(4*Pi^2) = 0.0000970457..., 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
44100 = 2^2 * 3^2 * 5^2 * 7^2 is a term since it has exactly 4 prime factors, 2, 3, 5 and 7, that are non-unitary.
MATHEMATICA
Select[Range[620000], Count[FactorInteger[#][[;; , 2]], _?(#1 > 1 &)] == 4 &]
CROSSREFS
Subsequence of A013929 and A318720.
Cf. A154945 (eta_1), A324833 (eta_2), A324834 (eta_3), A324835 (eta_4).
Sequence in context: A233790 A359127 A223457 * A190377 A049205 A234426
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 01 2020
STATUS
approved