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A377844
Numbers that have a single odd exponent larger than 1 in their prime factorization.
2
8, 24, 27, 32, 40, 54, 56, 72, 88, 96, 104, 108, 120, 125, 128, 135, 136, 152, 160, 168, 184, 189, 200, 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, 432, 440, 456, 459, 472, 480, 486, 488, 500
OFFSET
1,1
COMMENTS
First differs from A295661, A325990 and A376142 at n = 24: A295661(24) = A325990(24) = A376142(24) = 216 = 2^3 * 3^3 is not a term of this sequence.
Differs from A060476 by having the terms 432, 648, 1728, ..., and not having the terms 1, 216, 256, 768, 864, ... .
The asymptotic density of this sequence is Product_{p prime} (1 - 1/(p^2*(p+1))) * Sum_{p prime} (1/(p^3+p^2-1)) = 0.11498368544519741081... .
LINKS
MATHEMATICA
q[n_] := Count[FactorInteger[n][[;; , 2]], _?(# > 1 && OddQ[#] &)] == 1; Select[Range[500], q]
PROG
(PARI) is(k) = #select(x -> x>1 && x%2, factor(k)[, 2]) == 1;
CROSSREFS
Subsequence of A295661.
Subsequences: A065036, A143610, A163569.
Sequence in context: A060476 A295661 A376142 * A240111 A301517 A374459
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Nov 09 2024
STATUS
approved