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

1,1

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/zeta(k)) = 0.11615617754774636364... .

Links

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

Mathematica

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

Prog

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

Crossrefs

Complement of A368714 within A013929.

Cf. A051903, A060476, A295661, A325990.

Sequence in context: A325990 A060476 A295661 * A377844 A240111 A301517

Adjacent sequences: A376139 A376140 A376141 * A376143 A376144 A376145

Keyword

nonn,easy

Author

Amiram Eldar, Sep 11 2024

Status

approved