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

1,1

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

Formula

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

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 *)

Crossrefs

Cf. A001221, A006049, A045932.

Sequence in context: A172976 A171655 A293683 * A052402 A372076 A300041

Adjacent sequences: A006070 A006071 A006072 * A006074 A006075 A006076

Keyword

nonn

Author

N. J. A. Sloane

Status

approved