A375146 Numbers whose prime factorization has exactly one exponent that is larger than 3.

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... .

Links

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

Index entries for sequences computed from exponents in factorization of n.

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.

Cf. A013662, A057521, A190641, A246550, A375145.

Sequence in context: A048111 A122614 A046101 * A360723 A044856 A217558

Adjacent sequences: A375143 A375144 A375145 * A375147 A375148 A375149

Keyword

nonn,easy,new

Author

Amiram Eldar, Aug 01 2024

Status

approved