login
Numbers k such that k, k+1 and k+2 have exactly 2 distinct prime factors.
4

%I #15 Oct 01 2024 03:33:15

%S 20,33,34,38,44,50,54,55,56,74,75,85,86,91,92,93,94,98,115,116,117,

%T 122,133,134,141,142,143,144,145,146,158,159,160,175,176,183,187,200,

%U 201,205,206,207,212,213,214,215,216,217,224,235,247,248,295,296

%N Numbers k such that k, k+1 and k+2 have exactly 2 distinct prime factors.

%H Amiram Eldar, <a href="/A364307/b364307.txt">Table of n, a(n) for n = 1..10000</a>

%F {k: A001221(k) = A001221(k+1) = A001221(k+2) = 2}.

%e 44 = 2^2*11 has 2 distinct prime factors, and so has 45 = 3^2*5 and so has 46 = 2*23, so 44 is in the sequence.

%t q[n_] := q[n] = PrimeNu[n] == 2; Select[Range[300], q[#] && q[#+1] && q[#+2] &] (* _Amiram Eldar_, Oct 01 2024 *)

%Y Subsequence of A006073 and of A074851.

%Y Cf. A364308 (3 factors), A364309 (4 factors), A364266 (5 factors), A364265 (6 factors), A001221.

%K nonn

%O 1,1

%A _R. J. Mathar_, Jul 18 2023