A319923 Quasi-primes: composite numbers k such that the least prime factor is greater than k^(1/(log log k)^2).

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

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

Table of n, a(n) for n=1..56.

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,changed

Author

Alonso del Arte, Oct 01 2018

Status

approved