cp's OEIS Frontend

A375934 Numbers whose prime factorization has a second-largest exponent that equals 1.

%I A375934 #8 Sep 03 2024 01:17:53
%S A375934 12,18,20,24,28,40,44,45,48,50,52,54,56,60,63,68,75,76,80,84,88,90,92,
%T A375934 96,98,99,104,112,116,117,120,124,126,132,135,136,140,147,148,150,152,
%U A375934 153,156,160,162,164,168,171,172,175,176,180,184,188,189,192,198,204
%N A375934 Numbers whose prime factorization has a second-largest exponent that equals 1.
%C A375934 First differs from A332785 at n = 112: A332785(112) = 360 = 2^3 * 3^2 * 5 is not a term of this sequence.
%C A375934 First differs from A317616 at n = 38: A317616(38) = 144 = 2*4 * 3^2 is not a term of this sequence.
%C A375934 Numbers k such that A375933(k) = 1.
%C A375934 Numbers of the form s1 * s2^e, where s1 and s2 are coprime squarefree numbers that are both larger than 1, and e >= 2.
%C A375934 The asymptotic density of this sequence is Sum_{e>=2} d(e) = 0.36113984820338109927..., where d(e) = Product_{p prime} (1 - 1/p^2 + 1/p^e - 1/p^(e+1)) - Product_{p prime} (1 - 1/p^(e+1)) is the asymptotic density of terms k with A051903(k) = e >= 2.
%H A375934 Amiram Eldar, <a href="/A375934/b375934.txt">Table of n, a(n) for n = 1..10000</a>
%F A375934 A051904(a(n)) = 1.
%F A375934 A051903(a(n)) >= 2.
%F A375934 A001221(a(n)) = 2.
%t A375934 q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Max[0, Max[Select[e, # < Max[e] &]]] == 1]; Select[Range[300], q]
%o A375934 (PARI) is(n) = if(n == 1, 0, my(e = factor(n)[,2]); e = select(x -> x < vecmax(e), e); if(#e == 0, 0, vecmax(e) == 1));
%Y A375934 Equals A375142 \ A072777.
%Y A375934 Subsequence of A013929.
%Y A375934 Subsequences: A054753, A065036, A072357, A095990, A096156, A178739, A178740, A179664, A179668, A179692, A189987, A360793, A375076.
%Y A375934 Cf. A001221, A005117, A051903, A051904, A072777, A317616, A332785, A375142, A375933.
%K A375934 nonn,easy
%O A375934 1,1
%A A375934 _Amiram Eldar_, Sep 03 2024