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A375146
Numbers whose prime factorization has exactly one exponent that is larger than 3.
2
16, 32, 48, 64, 80, 81, 96, 112, 128, 144, 160, 162, 176, 192, 208, 224, 240, 243, 256, 272, 288, 304, 320, 324, 336, 352, 368, 384, 400, 405, 416, 432, 448, 464, 480, 486, 496, 512, 528, 544, 560, 567, 576, 592, 608, 624, 625, 640, 648, 656, 672, 688, 704, 720
OFFSET
1,1
COMMENTS
Subsequence of A046101 and first differs from it at n = 98: A046101(98) = 1296 = 2^4 * 3^4 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 3 (A246550).
The asymptotic density of this sequence is (1/zeta(4)) * Sum_{p prime} 1/(p^4-1) = 0.075131780079404733755... .
EXAMPLE
16 = 2^4 is a term since its prime factorization has exactly one exponent, 4, that is larger than 3.
MATHEMATICA
q[n_] := Count[FactorInteger[n][[;; , 2]], _?(# > 3 &)] == 1; Select[Range[1000], q]
PROG
(PARI) is(k) = #select(x -> x > 3, factor(k)[, 2]) == 1;
CROSSREFS
Subsequence of A046101.
Sequence in context: A048111 A122614 A046101 * A360723 A044856 A217558
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 01 2024
STATUS
approved