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A334213 Numbers m such that m^k + 1 is squarefree for all 0 <= k <= m. 2

%I

%S 0,1,2,4,6,10,16,30,36,46,256

%N Numbers m such that m^k + 1 is squarefree for all 0 <= k <= m.

%C m = 2^i is a term iff k*i is not in A049096 with 0 < k < m + 1. Up to i = 128, there are no more terms of the form 2^i. a(12) > 10^7, if it exists. - _Jinyuan Wang_, May 01 2020

%e 4^0 + 1 = 2 is squarefree, 4^1 + 1 = 5 is squarefree, 4^2 + 1 = 17 is squarefree, 4^3 + 1 = 5*13 is squarefree and 4^4 + 1 = 257 is squarefree, so 4 is in the sequence.

%t Do[L=Length[a];a=Select[a=m^Range[0,m-1]+1,SquareFreeQ[#]&];If[L==m-1,Print[m-1]],{m,0,1000}] (* _Metin Sariyar_, Apr 21 2020 *)

%o (PARI) isOK(m) = k=0; until(k>m, if(!issquarefree(m^k+1), return(0)); k++); 1;

%o for(m=0, 99, if(isOK(m), print1(m, ", ")))

%Y Cf. A049096, A334212, A334214.

%K nonn,more

%O 1,3

%A _Gionata Neri_, Apr 18 2020

%E a(11) from _Jinyuan Wang_, May 01 2020

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Last modified October 17 13:24 EDT 2021. Contains 348049 sequences. (Running on oeis4.)