A381315 Numbers whose prime factorization exponents include exactly one 3 and no exponent greater than 3.

8, 24, 27, 40, 54, 56, 72, 88, 104, 108, 120, 125, 135, 136, 152, 168, 184, 189, 200, 232, 248, 250, 264, 270, 280, 296, 297, 312, 328, 343, 344, 351, 360, 375, 376, 378, 392, 408, 424, 440, 456, 459, 472, 488, 500, 504, 513, 520, 536, 540, 552, 568, 584, 594

Offset

1,1

Comments

Subsequence of A176297 and A375072, and first differs from them at n = 20: A176297(20) = A375072(20) = 216 = 2^3 * 3^3 is not a term of this sequence.

The asymptotic density of this sequence is (1/zeta(3)) * Sum_{p prime} 1/(p+p^2+p^3) = 0.089602607198058453295... .

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, MemberQ[e, 3] && Count[e, _?(# < 3 &)] == Length[e] - 1]; Select[Range[600], q]

Prog

(PARI) isok(k) = {my(e = factor(k)[, 2]~); select(x -> x > 2, e) == [3]; }

Crossrefs

Subsequence of A046100, A176297, A375072 and A375145.

Subsequences: A030078, A048109, A065036, A143610, A163569, A179670, A179695, A179700, A189975, A189984, A190109, A190378, A190382.

Cf. A002117.

Sequence in context: A336593 A176297 A375072 * A175496 A048109 A068781

Adjacent sequences: A381312 A381313 A381314 * A381316 A381317 A381320

Keyword

nonn,easy,new

Author

Amiram Eldar, Feb 19 2025

Status

approved