A376251 - OEIS

%I #6 Sep 20 2024 06:11:46

%S 12,18,20,28,44,45,50,52,60,63,68,72,75,76,84,90,92,98,99,108,116,117,

%T 124,126,132,140,147,148,150,153,156,164,171,172,175,180,188,198,200,

%U 204,207,212,220,228,234,236,242,244,245,252,260,261,268,275,276,279

%N Numbers that have a second-largest exponent in their prime factorization and it is smaller by 1 than the largest exponent.

%C First differs from its subsequence A325241 at n = 74: a(74) = 360 = 2^3 * 3^2 * 5 is not a term of A325241.

%C Numbers k such that 0 < A375933(k) = A051903(k) - 1.

%C The asymptotic density of this sequence is Sum_{k>=2} d(k) = 0.24179287499021146826..., where d(2) = 1/zeta(3) - 1/zeta(2), and d(k) = 1/zeta(k+1) - 1/zeta(k) + 1/zeta(k-1) - Product_{p prime} (1 - 1/p^(k-1) + 1/p^k - 1/p^(k+1)) for k >= 3.

%H Amiram Eldar, <a href="/A376251/b376251.txt">Table of n, a(n) for n = 1..10000</a>

%t q[k_] := Module[{e = Union[FactorInteger[k][[;; , 2]]]}, Length[e] > 1 && e[[-2]] + 1 == e[[-1]]]; Select[Range[300], q]

%o (PARI) is(k) = {my(e = Set(factor(k)[, 2])); #e > 1 && e[#e-1] + 1 == e[#e]; }

%Y Subsequence of A013929.

%Y Subsequences: A067259, A325241, A376249.

%Y Cf. A002117, A013661, A051903, A375933.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Sep 17 2024