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%I #9 Sep 21 2023 06:29:33
%S 423,475,1323,1375,1519,2007,2223,2275,2871,3123,3175,3211,3283,3479,
%T 3575,3751,3771,4023,4075,4475,4923,4959,4975,5047,5535,5823,5875,
%U 6723,6775,6811,7299,7623,7675,8107,8379,8523,8575,8955,9423,9475,10323,10339,10375,10467
%N Starts of runs of 3 consecutive integers that are divisible by the square of their least prime factor.
%C Numbers k such that k, k+1 and k+2 are all terms of A283050.
%C Numbers of the form 4*k+2 are not terms of A283050. Therefore, there are no runs of 4 or more consecutive integers, and all the terms of this sequence are of the form 4*k+3.
%C The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 2, 40, 429, 4419, 44352, 444053, 4441769, 44421000, 444220814, ... . Apparently, the asymptotic density of this sequence exists and equals 0.004442... .
%H Amiram Eldar, <a href="/A365865/b365865.txt">Table of n, a(n) for n = 1..10000</a>
%e 423 is a term since 3 is the least prime factor of 423 and 423 is divisible by 3^2 = 9, 2 is the least prime factor of 424 and 424 is divisible by 2^2 = 4, and 5 is the least prime factor of 425 and 425 is divisible by 5^2 = 25.
%t Select[4 * Range[2700] + 3, AllTrue[# + {0, 1, 2}, FactorInteger[#1][[1, -1]] >= 2 &] &]
%o (PARI) is(n) = factor(n)[1,2] >= 2;
%o lista(kmax) = forstep(k = 3, kmax, 4, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));
%Y Cf. A067029.
%Y Subsequence of A004767, A070258, A283050 and A365864.
%K nonn,easy
%O 1,1
%A _Amiram Eldar_, Sep 21 2023
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