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A334214 Odd numbers m such that m^k + 1 is squarefree for all 0 <= k <= (m - 1)/2. 2
1, 5, 9, 13, 21, 25, 85, 105, 165 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)