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

1,1

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.

Numbers k such that the powerful part of k, A057521(k), is a prime power whose exponent is larger than 2 (A246549).

The asymptotic density of this sequence is (1/zeta(3)) * Sum_{p prime} 1/(p^3-1) = A286229 / A002117 = 0.16148833663564192901... .

Links

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

Index entries for sequences computed from exponents in factorization of n.

Example

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

Mathematica

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

Prog

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

Crossrefs

Subsequence of A046099.

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

Sequence in context: A228957 A137845 A046099 * A344653 A345193 A365866

Adjacent sequences: A375142 A375143 A375144 * A375146 A375147 A375148

Keyword

nonn,easy

Author

Amiram Eldar, Aug 01 2024

Status

approved