A334212 -id:A334212 - cp's OEIS frontend

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

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

Offset: 1

Gionata Neri, Apr 18 2020

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

			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.

Cf. A049096, A334212, A334214.

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 *)

isOK(m) = k=0; until(k>m, if(!issquarefree(m^k+1), return(0)); k++); 1;
for(m=0, 99, if(isOK(m), print1(m, ", ")))

a(11) from Jinyuan Wang, May 01 2020

A334214 Odd numbers m such that m^k + 1 is squarefree for all 0 <= k <= (m - 1)/2.

Original entry on oeis.org

1, 5, 9, 13, 21, 25, 85, 105, 165

Offset: 1

Gionata Neri, Apr 18 2020

a(10) > 10000, if it exists. Most of the relevant factorizations of 165^k+1 were already present in the FactorDB database. The factorization of 165^79+1 has been completed with the software CADO-NFS. - Giovanni Resta, Apr 22 2020

Cf. A334212, A334213.

isOK(m) = k=0; until(k>(m-1)/2, if(!issquarefree(m^k+1), return(0)); k++); 1;
for(m=0, 140, if(isOK(m)&&m%2==1, print1(m, ", ")))

a(9) from Giovanni Resta, Apr 22 2020

cp's OEIS Frontend

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

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