cp's OEIS Frontend

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

%I A375146 #15 Aug 02 2024 08:57:35
%S A375146 16,32,48,64,80,81,96,112,128,144,160,162,176,192,208,224,240,243,256,
%T A375146 272,288,304,320,324,336,352,368,384,400,405,416,432,448,464,480,486,
%U A375146 496,512,528,544,560,567,576,592,608,624,625,640,648,656,672,688,704,720
%N A375146 Numbers whose prime factorization has exactly one exponent that is larger than 3.
%C A375146 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.
%C A375146 Numbers k such that the powerful part of k, A057521(k), is a prime power whose exponent is larger than 3 (A246550).
%C A375146 The asymptotic density of this sequence is (1/zeta(4)) * Sum_{p prime} 1/(p^4-1) = 0.075131780079404733755... .
%H A375146 Amiram Eldar, <a href="/A375146/b375146.txt">Table of n, a(n) for n = 1..10000</a>
%H A375146 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%e A375146 16 = 2^4 is a term since its prime factorization has exactly one exponent, 4, that is larger than 3.
%t A375146 q[n_] := Count[FactorInteger[n][[;;, 2]], _?(# > 3 &)] == 1; Select[Range[1000], q]
%o A375146 (PARI) is(k) = #select(x -> x > 3, factor(k)[, 2]) == 1;
%Y A375146 Subsequence of A046101.
%Y A375146 Cf. A013662, A057521, A190641, A246550, A375145.
%K A375146 nonn,easy
%O A375146 1,1
%A A375146 _Amiram Eldar_, Aug 01 2024