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 A319923 Quasi-primes: composite numbers k such that the least prime factor is greater than k^(1/(log log k)^2). 0
 121, 133, 143, 161, 169, 187, 203, 209, 217, 221, 247, 253, 259, 287, 289, 299, 301, 319, 323, 329, 341, 343, 361, 371, 377, 391, 403, 407, 413, 427, 437, 451, 469, 473, 481, 493, 497, 511, 517, 527, 529, 533, 539, 551, 553, 559, 581, 583, 589, 611, 623, 629, 637, 649, 667, 671 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Obviously the least prime factor of a composite number k can't be greater than sqrt(k). However, it can be greater than some function that grows more slowly than sqrt(k); k^(1/(log log k)^2) is just one possibility. LINKS Encyclopedia of Mathematics, Quasi-prime number EXAMPLE 539 = 7^2 * 11, and 539^(1/(log log 539)^2) = 6.42358133145183..., which is less than least prime factor 7. Hence 539 is in the sequence. 540 = 2^2 * 3^3 * 5, and 540^(1/(log log 540)^2 = 6.423273267433689..., which is greater than least prime factor 2, so 540 is not in the sequence. MATHEMATICA Select[Range[1000], Not[PrimeQ[#]] && FactorInteger[#][[1, 1]] > #^(1/Log[Log[#]]^2) &] CROSSREFS Cf. A251728. Sequence in context: A044867 A162531 A050697 * A020253 A182776 A080466 Adjacent sequences: A319920 A319921 A319922 * A319924 A319925 A319926 KEYWORD nonn AUTHOR Alonso del Arte, Oct 01 2018 STATUS approved

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Last modified March 23 10:25 EDT 2023. Contains 361443 sequences. (Running on oeis4.)