# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a365871 Showing 1-1 of 1 %I A365871 #9 Sep 21 2023 06:29:04 %S A365871 475,1519,2223,2275,3283,4475,4923,4975,5823,6723,6811,7299,7675,8107, %T A365871 8379,8523,8955,9475,10323,10467,11275,12427,12463,12591,13075,13867, %U A365871 13923,14355,15631,15723,16675,18027,18275,18475,18767,19323,19375,19647,22075,22831 %N A365871 Starts of runs of 3 consecutive integers whose exponent of least prime factor in their prime factorization is even. %C A365871 Numbers k such that k, k+1 and k+2 are all terms of A365869. %C A365871 Numbers of the form 4*k+2 are not terms of A365869. 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 A365871 The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 1, 18, 195, 1952, 19542, 195514, 1955859, 19560453, 195611458, ... . Apparently, the asymptotic density of this sequence exists and equals 0.001956... . %H A365871 Amiram Eldar, Table of n, a(n) for n = 1..10000 %e A365871 475 is a term since the exponent of the prime factor 5 in the factorization 475 = 5^2 * 19 is 2, which is even, the exponent of the prime factor 2 in the factorization 476 = 2^2 * 7 * 17 is 2, which is even, and the exponent of the prime factor 3 in the factorization 477 = 3^2 * 53 is also 2, which is even. %t A365871 Select[4 * Range[6000] + 3, AllTrue[# + {0, 1, 2}, EvenQ[FactorInteger[#1][[1, -1]]] &] &] %o A365871 (PARI) is(n) = !(factor(n)[1,2]%2); %o A365871 lista(kmax) = forstep(k = 3, kmax, 4, if(is(k) && is(k+1) && is(k+2), print1(k, ", "))); %Y A365871 Cf. A067029. %Y A365871 Subsequence of A004767, A365869 and A365870. %K A365871 nonn,easy %O A365871 1,1 %A A365871 _Amiram Eldar_, Sep 21 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE