A364307 Numbers k such that k, k+1 and k+2 have exactly 2 distinct prime factors.

20, 33, 34, 38, 44, 50, 54, 55, 56, 74, 75, 85, 86, 91, 92, 93, 94, 98, 115, 116, 117, 122, 133, 134, 141, 142, 143, 144, 145, 146, 158, 159, 160, 175, 176, 183, 187, 200, 201, 205, 206, 207, 212, 213, 214, 215, 216, 217, 224, 235, 247, 248, 295, 296

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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

Example

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.

Mathematica

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

Crossrefs

Subsequence of A006073 and of A074851.

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

Sequence in context: A124665 A134989 A119873 * A075230 A165236 A067468

Adjacent sequences: A364304 A364305 A364306 * A364308 A364309 A364310

Keyword

nonn

Author

R. J. Mathar, Jul 18 2023

Status

approved