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Numbers k such that k, k+1 and k+2 have exactly 4 distinct prime factors.
5

%I #19 Oct 01 2024 03:05:54

%S 37960,44484,45694,50140,51428,55130,55384,61334,63364,64294,67164,

%T 68264,68474,70004,70090,71708,72708,76152,80444,81548,81718,82040,

%U 84434,85490,86240,90363,95380,97382,98020,99084,99384,99428,99788,100164,100490,100594,102254,102542,104804,105994,108204

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

%H David A. Corneth, <a href="/A364309/b364309.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1) = A087966(3).

%F a(n)+1 = A168628(n).

%F {k: A001221(k) = A001221(k+1) = A001221(k+2) = 4}.

%e 37960 = 2^3*5*13*73, 37961 = 7*11*17*29, and 37962 = 2*3^3*19*37 each have 4 distinct prime factors, so 37960 is in the sequence.

%t q[n_] := q[n] = PrimeNu[n] == 4; Select[Range[10^5], q[#] && q[#+1] && q[#+2] &] (* _Amiram Eldar_, Oct 01 2024 *)

%Y Subsequence of A006073 and of A140078.

%Y A176167 is a subsequence.

%Y Cf. A364307 (2 factors), A364308 (3 factors), A364266 (5 factors), A364265 (6 factors), A001221, A087966, A168628.

%K nonn

%O 1,1

%A _R. J. Mathar_, Jul 18 2023