login
Nonprime squarefree numbers n such that both n-1 and n+1 are not squarefree and not prime.
4

%I #14 Jun 17 2022 17:26:19

%S 26,51,55,91,161,170,235,249,295,305,339,341,362,377,413,415,451,485,

%T 489,530,551,559,579,595,629,638,649,651,665,667,685,687,703,721,723,

%U 737,749,849,851,874,917,926,949,951,955,962,989,1015,1027,1057,1059

%N Nonprime squarefree numbers n such that both n-1 and n+1 are not squarefree and not prime.

%H Harvey P. Dale, <a href="/A073249/b073249.txt">Table of n, a(n) for n = 1..1000</a>

%t npsQ[n_]:=SquareFreeQ[n]&&NoneTrue[n+{1,0,-1},PrimeQ]&&NoneTrue[n+{1,-1},SquareFreeQ]; Select[Range[2000],npsQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 20 2019 *)

%t Mean/@SequencePosition[Table[Which[CompositeQ[n]&&SquareFreeQ[n],1,!SquareFreeQ[ n] && CompositeQ[ n],-1,True,0],{n,1100}],{-1,1,-1}] (* _Harvey P. Dale_, Jun 17 2022 *)

%Y Cf. A000469, A005117, A073247, A073250, A073251.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 22 2002

%E Corrected by _Harvey P. Dale_, Jan 20 2019