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%I #7 Mar 30 2024 05:33:02
%S 4,8,9,12,16,20,24,25,27,28,32,36,40,44,45,48,49,52,56,60,63,64,68,72,
%T 76,80,81,84,88,92,96,99,100,104,108,112,116,117,120,121,124,125,128,
%U 132,135,136,140,144,148,152,153,156,160,164,168,169,171,172,175,176
%N Nonsquarefree numbers whose largest nonunitary prime divisor is smaller than their smallest unitary prime divisor, if it exists.
%C Subsequence of A283050 and first differs from it at n = 100: A283050(100) = 300 = 2^2 * 3 * 5^2 is not a term of this sequence.
%C Powerful numbers and nonpowerful numbers k such that 1 < A249740(k) < A277698(k), or equivalently, 1 < A006530(A057521(k)) < A020639(A055231(k)).
%C The asymptotic density of this sequence is (6/Pi^2) * Sum_{p prime} f(p)/(p^2-p+1) = 0.32131800923..., where f(p) = Product_{primes q <= p} (q^2-q+1)/(q^2-1).
%H Amiram Eldar, <a href="/A371601/b371601.txt">Table of n, a(n) for n = 1..10000</a>
%t q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Max[e] > 1 && (Min[e] > 1 || Max[e[[FirstPosition[e, 1][[1]] ;; -1]]] == 1)]; Select[Range[200], q]
%o (PARI) is(n) = {my(e = apply(x->if(x > 1, 2, 1), factor(n)[,2])); n > 1 && vecmax(e) > 1 && vecsort(e, , 4) == e;}
%Y Subsequence of A013929 and A283050.
%Y Cf. A001694, A006530, A020639, A052485, A055231, A057521, A059956, A249740, A277698.
%K nonn,easy
%O 1,1
%A _Amiram Eldar_, Mar 29 2024
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