A375145 -id:A375145 - cp's OEIS frontend

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

Amiram Eldar, Feb 19 2025

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... .

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

Subsequence of A046100, A176297, A375072 and A375145.
Subsequences: A030078, A048109, A065036, A143610, A163569, A179670, A179695, A179700, A189975, A189984, A190109, A190378, A190382.
Cf. A002117.

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

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

A375146 Numbers whose prime factorization has exactly one exponent that is larger than 3.

Original entry on oeis.org

16, 32, 48, 64, 80, 81, 96, 112, 128, 144, 160, 162, 176, 192, 208, 224, 240, 243, 256, 272, 288, 304, 320, 324, 336, 352, 368, 384, 400, 405, 416, 432, 448, 464, 480, 486, 496, 512, 528, 544, 560, 567, 576, 592, 608, 624, 625, 640, 648, 656, 672, 688, 704, 720

Offset: 1

Amiram Eldar, Aug 01 2024

Subsequence of A046101 and first differs from it at n = 98: A046101(98) = 1296 = 2^4 * 3^4 is not a term of this sequence.
Numbers k such that the powerful part of k, A057521(k), is a prime power whose exponent is larger than 3 (A246550).
The asymptotic density of this sequence is (1/zeta(4)) * Sum_{p prime} 1/(p^4-1) = 0.075131780079404733755... .

			16 = 2^4 is a term since its prime factorization has exactly one exponent, 4, that is larger than 3.

Subsequence of A046101.

Cf. A013662, A057521, A190641, A246550, A375145.

q[n_] := Count[FactorInteger[n][[;;, 2]], _?(# > 3 &)] == 1; Select[Range[1000], q]

is(k) = #select(x -> x > 3, factor(k)[, 2]) == 1;

cp's OEIS Frontend

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

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