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Numbers k such that k, k+1 and k+2 all have the same number of distinct prime divisors.
21

%I #29 Jun 12 2024 18:49:44

%S 2,3,7,20,33,34,38,44,50,54,55,56,74,75,85,86,91,92,93,94,98,115,116,

%T 117,122,133,134,141,142,143,144,145,146,158,159,160,175,176,183,187,

%U 200,201,205,206,207,212,213,214,215,216,217,224,235,247

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

%C Distinct prime divisors means that the prime divisors are counted without multiplicity. - _Harvey P. Dale_, Apr 19 2011

%H Harvey P. Dale, <a href="/A006073/b006073.txt">Table of n, a(n) for n = 1..10000</a>

%F Union of {2,3,7} and A364307 and A364308 and A364309 and A364266 and A364265 etc. - _R. J. Mathar_, Jul 18 2023

%t pdQ[n_]:=PrimeNu[n]==PrimeNu[n+1]==PrimeNu[n+2]; Select[Range[250], pdQ] (* _Harvey P. Dale_, Apr 19 2011 *)

%t 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 *)

%t Flatten[Position[Partition[PrimeNu[Range[250]],3,1],_?(#[[1]]==#[[2]]== #[[3]]&),{1},Heads->False]] (* _Harvey P. Dale_, Oct 30 2013 *)

%t SequencePosition[PrimeNu[Range[250]],{x_,x_,x_}][[;;,1]] (* _Harvey P. Dale_, Jun 12 2024 *)

%Y Cf. A001221, A006049, A045932.

%K nonn

%O 1,1

%A _N. J. A. Sloane_