A375145 Numbers whose prime factorization has exactly one exponent that is larger than 2.

8, 16, 24, 27, 32, 40, 48, 54, 56, 64, 72, 80, 81, 88, 96, 104, 108, 112, 120, 125, 128, 135, 136, 144, 152, 160, 162, 168, 176, 184, 189, 192, 200, 208, 224, 232, 240, 243, 248, 250, 256, 264, 270, 272, 280, 288, 296, 297, 304, 312, 320, 324, 328, 336, 343, 344

Offset: 1

Author

Amiram Eldar, Aug 01 2024

Keywords

• nonn
• easy

Comments

Subsequence of A046099 and first differs from it at n = 35: A046099(35) = 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^3-1) = A286229 / A002117 = 0.16148833663564192901... .

Examples

			8 = 2^3 is a term since its prime factorization has exactly one exponent, 3, that is larger than 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Subsequence of A046099, A356862.

Cf. A002117, A057521, A190641, A246549, A286229, A375146.

Programs

Mathematica

q[n_] := Count[FactorInteger[n][[;; , 2]], _?(# > 2 &)] == 1; Select[Range[350], q]

PARI

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