cp's OEIS Frontend

A365868 Starts of runs of 3 consecutive integers that are divisible by the cube of their least prime factor.

%I A365868 #15 Sep 21 2023 06:29:22
%S A365868 1375,16119,25623,28375,52623,55375,57967,79623,82375,90207,94471,
%T A365868 106623,109375,129623,133623,134431,136375,160623,163375,164295,
%U A365868 187623,190375,206143,214623,217375,241623,244375,268623,271375,280231,295623,298375,312471,322623,325375
%N A365868 Starts of runs of 3 consecutive integers that are divisible by the cube of their least prime factor.
%C A365868 Numbers k such that k, k+1 and k+2 are all terms of A365866.
%C A365868 Numbers of the form 4*k+2 are not terms of A365866. Therefore, there are no runs of 4 or more consecutive integers. Since the middle integer in each triple is divisible by 8, all the terms of this sequence are of the form 8*k+7.
%C A365868 The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are , 1, 11, 109, 1092, 10899, 109125, 1091335, 10912897, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0001091... .
%H A365868 Amiram Eldar, <a href="/A365868/b365868.txt">Table of n, a(n) for n = 1..10000</a>
%e A365868 1375 is a term since 5 is the least prime factor of 1375 and 1375 is divisible by 5^3 = 125, 2 is the least prime factor of 1376 and 1376 is divisible by 2^3 = 8, and 3 is the least prime factor of 1377 and 1377 is divisible by 3^3 = 27.
%t A365868 Select[8 * Range[41000] + 7, AllTrue[# + {0, 1, 2}, FactorInteger[#1][[1, -1]] >= 3 &] &]
%o A365868 (PARI) is(n) = factor(n)[1,2] >= 3;
%o A365868 lista(kmax) = forstep(k = 7, kmax, 8, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));
%Y A365868 Cf. A067029.
%Y A365868 Subsequence of A004771, A068140, A365866 and A365867.
%K A365868 nonn,easy
%O A365868 1,1
%A A365868 _Amiram Eldar_, Sep 21 2023