A364309 Numbers k such that k, k+1 and k+2 have exactly 4 distinct prime factors.

37960, 44484, 45694, 50140, 51428, 55130, 55384, 61334, 63364, 64294, 67164, 68264, 68474, 70004, 70090, 71708, 72708, 76152, 80444, 81548, 81718, 82040, 84434, 85490, 86240, 90363, 95380, 97382, 98020, 99084, 99384, 99428, 99788, 100164, 100490, 100594, 102254, 102542, 104804, 105994, 108204

Offset: 1

Author

R. J. Mathar, Jul 18 2023

Keywords

• nonn

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A006073 and of A140078.

A176167 is a subsequence.

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

Programs

Mathematica

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

Formula

a(1) = A087966(3).

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

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