This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376249 #10 Sep 20 2024 06:11:20
%S A376249 12,18,20,28,44,45,50,52,60,63,68,72,75,76,84,90,92,98,99,108,116,117,
%T A376249 124,126,132,140,147,148,150,153,156,164,171,172,175,188,198,200,204,
%U A376249 207,212,220,228,234,236,242,244,245,260,261,268,275,276,279,284,292,294
%N A376249 Numbers that are not prime powers and have a unique largest prime exponent that is larger than the second-largest prime exponent by 1.
%C A376249 First differs from A325241 at n = 36: A325241(36) = 2^2 * 3^2 * 5 is not a term of this sequence. Also, a(71) = 360 = 2^3 * 3^2 * 5 is the least term that is not a term of A325241.
%C A376249 Numbers whose unordered prime signature (i.e., sorted, see A118914) ends with two consecutive integers: {..., k, k+1} for some k >= 1.
%C A376249 The asymptotic density of this sequence is Sum_{k >= 1, p prime} (d(k+1, p) - d(k, p))/p^(k+1) = 0.21831645263800520483..., where d(k, p) = 0 for k = 1, and (1-1/p)/((1-1/p^k)*zeta(k)) for k > 1, is the density of terms that have in their prime factorization a prime p with the largest exponent that is > k.
%H A376249 Amiram Eldar, <a href="/A376249/b376249.txt">Table of n, a(n) for n = 1..10000</a>
%t A376249 q[k_] := Module[{e = Sort[FactorInteger[k][[;; , 2]]]}, Length[e] > 1 && e[[-1]] == e[[-2]] + 1]; Select[Range[300], q]
%o A376249 (PARI) is(k) = {my(e = vecsort(factor(k)[, 2])); #e > 1 && e[#e] == e[#e-1] + 1;}
%Y A376249 Subsequence of A356862.
%Y A376249 Subsequences: A054753, A072357, A095990, A096156, A143610, A163569, A179666, A179702.
%Y A376249 Cf. A118914, A246655, A325241.
%K A376249 nonn,easy
%O A376249 1,1
%A A376249 _Amiram Eldar_, Sep 16 2024