A376142 Nonsquarefree numbers whose prime factorization has a maximum exponent that is odd.

8, 24, 27, 32, 40, 54, 56, 72, 88, 96, 104, 108, 120, 125, 128, 135, 136, 152, 160, 168, 184, 189, 200, 216, 224, 232, 243, 248, 250, 264, 270, 280, 288, 296, 297, 312, 328, 343, 344, 351, 352, 360, 375, 376, 378, 384, 392, 408, 416, 424, 440, 456, 459, 472, 480, 486, 488, 500

Offset: 1

Author

Amiram Eldar, Sep 11 2024

Keywords

• nonn
• easy

Comments

Subsequence of A060476 and differs from it by not having the terms 1, 256, 768, 1280, 1792, 2304, ... .

Subsequence of A295661 and first differs from it at n = 51: A295661(51) = 432 is not a term of this sequence.

First differs from A325990 at n = 30: A325990(30) = 256 is not a term of this sequence.

Nonsquarefree numbers k such that A051903(k) is odd, or equivalently, numbers k such that A051903(k) is an odd number that is larger than 1.

The asymptotic density of this sequence is Sum_{k>=3} (-1)^(k+1) * (1 - 1/zeta(k)) = 0.11615617754774636364... .

Links

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

Crossrefs

Complement of A368714 within A013929.

Cf. A051903, A060476, A295661, A325990.

Programs

Mathematica

q[n_] := n > 1 && OddQ[n]; Select[Range[500], q[Max[FactorInteger[#][[;; , 2]]]] &]

PARI

is(k) = k > 1 && apply(x -> (x > 1 && x % 2), vecmax(factor(k)[, 2]));