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A376142
Nonsquarefree numbers whose prime factorization has a maximum exponent that is odd.
2
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
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.
Sequence in context: A325990 A060476 A295661 * A240111 A301517 A374459
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 11 2024
STATUS
approved