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

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

Offset: 1

Author

Gionata Neri, Apr 18 2020

Keywords

• nonn
• more
• hard

Comments

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

Crossrefs

Cf. A334212, A334213.

Programs

PARI

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, ", ")))

Extensions

a(9) from Giovanni Resta, Apr 22 2020