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%I #13 Dec 18 2023 01:46:21
%S 12,20,28,44,45,52,60,63,68,76,84,92,99,116,117,124,132,140,148,153,
%T 156,164,171,172,175,188,204,207,212,220,228,236,244,260,261,268,275,
%U 276,279,284,292,308,315,316,325,332,333,340,348,356,364,369,372,380,387
%N Numbers of the form p^2 * m, squarefree m > 1, prime p < lpf(m), where lpf(m) = A020639(m).
%C Proper subset of A126706. Proper subset of A364996.
%C Prime signature of a(n) is 2 followed by at least one 1.
%C Numbers of the form A065642(A120944(k)) for some k.
%C The asymptotic density of this sequence is (6/Pi^2) * Sum_{p prime} (1/p^2) * (Product_{primes q <= p} (q/(q+1))) = 0.155068688392... . - _Amiram Eldar_, Dec 18 2023
%H Michael De Vlieger, <a href="/A366825/b366825.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 12 = 4*3 = p^2 * m, squarefree m > 1; sqrt(4) < lpf(3), i.e., 2 < 3.
%e a(5) = 45 = 9*5 = p^2 * m, squarefree m > 1; sqrt(9) < lpf(5), i.e., 3 < 5.
%e Prime powers p^k, k > 2, are not in the sequence since m = p^(k-2) is not squarefree and p = lpf(m).
%t Select[Select[Range[500], PrimeOmega[#] > PrimeNu[#] > 1 &], First[#1] == 2 && Union[#2] == {1} & @@ TakeDrop[FactorInteger[#][[All, -1]], 1] &]
%o (PARI) is(n) = {my(e = factor(n)[, 2]); #e > 1 && e[1] == 2 && vecmax(e[2..#e]) == 1;} \\ _Amiram Eldar_, Dec 18 2023
%Y Cf. A007947, A020639, A065642, A120944, A126706, A364996.
%K nonn,easy
%O 1,1
%A _Michael De Vlieger_, Dec 15 2023
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