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

1,2

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

Links

Table of n, a(n) for n=1..9.

Prog

(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, ", ")))

Crossrefs

Cf. A334212, A334213.

Sequence in context: A314792 A089217 A166049 * A053411 A332571 A023382

Adjacent sequences: A334211 A334212 A334213 * A334215 A334216 A334217

Keyword

nonn,more,hard

Author

Gionata Neri, Apr 18 2020

Extensions

a(9) from Giovanni Resta, Apr 22 2020

Status

approved