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

Author

Amiram Eldar, Aug 01 2024

Keywords

• nonn
• easy

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... .

Examples

			16 = 2^4 is a term since its prime factorization has exactly one exponent, 4, that is larger than 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Subsequence of A046101.

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

Programs

Mathematica

q[n_] := Count[FactorInteger[n][[;;, 2]], _?(# > 3 &)] == 1; Select[Range[1000], q]

PARI

is(k) = #select(x -> x > 3, factor(k)[, 2]) == 1;