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

1,1

Links

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

Formula

a(1) = A087966(3).

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

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

Example

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.

Mathematica

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

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.

Sequence in context: A102332 A172425 A224906 * A168628 A178286 A187938

Adjacent sequences: A364306 A364307 A364308 * A364310 A364311 A364312

Keyword

nonn

Author

R. J. Mathar, Jul 18 2023

Status

approved