A006073 Numbers k such that k, k+1 and k+2 all have the same number of distinct prime divisors.

2, 3, 7, 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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Distinct prime divisors means that the prime divisors are counted without multiplicity. - Harvey P. Dale, Apr 19 2011

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A006049, A045932.

Programs

Mathematica

pdQ[n_]:=PrimeNu[n]==PrimeNu[n+1]==PrimeNu[n+2]; Select[Range[250], pdQ] (* Harvey P. Dale, Apr 19 2011 *)
Take[Transpose[Flatten[Select[Partition[{#,PrimeNu[#]}&/@Range[250000], 3,1],#[[1,2]]==#[[2,2]]==#[[3,2]]&],1]][[1]],{1,-1,3}] (* Harvey P. Dale, Dec 09 2011 *)
Flatten[Position[Partition[PrimeNu[Range[250]],3,1],?(#[[1]]==#[[2]]== #[[3]]&),{1},Heads->False]] (* _Harvey P. Dale, Oct 30 2013 *)
SequencePosition[PrimeNu[Range[250]],{x_,x_,x_}][[;;,1]] (* Harvey P. Dale, Jun 12 2024 *)

Formula

Union of {2,3,7} and A364307 and A364308 and A364309 and A364266 and A364265 etc. - R. J. Mathar, Jul 18 2023