A083955 Numbers n > 1 such that n^5 - 2 has no prime factor > n.

3557, 12038, 14810, 15424, 28456, 30742, 31540, 37665, 45602, 46883, 47879, 48152, 52196, 52617, 55265, 57902, 68306, 69032, 74925, 76262, 79562, 79984, 84569, 90442, 104867, 104956, 107213, 112570, 114614, 119477, 127634, 131072, 132466

Offset

1,1

Comments

Also integers n > 1 for which there is no prime p > n such that x = n is a solution mod p of x^5 = 2, since the following equivalences hold for n > 1: There is a prime p > n such that n is a solution mod p of x^5 = 2 iff n^5 - 2 has a prime factor > n; n is a solution mod p of x^5 = 2 iff p is a prime factor of n^5 - 2 and p > n.

Links

Table of n, a(n) for n=1..33.

Example

12038 is a term since 12038^5 - 2 = 252796871460867395166 = 2*3*3*3*263*571*641*911*5849*9127 has no prime factor > 12038.

Mathematica

t = {}; Do[If[Max[First/@FactorInteger[n^5-2]]<n, AppendTo[t, n]], {n, 2, 5*10^4}]; t (* Jayanta Basu, May 20 2013 *)
Select[Range[2, 133000], Max[FactorInteger[#^5-2][[;; , 1]]]<=#&] (* Harvey P. Dale, Mar 02 2023 *)

Prog

(PARI) {for(n=2, 133000, f=factor(n^5-2); if(f[matsize(f)[1], 1]<=n, print1(n, ", ")))}

Crossrefs

Cf. A040159, A040160, A065903.

Sequence in context: A218815 A248855 A151810 * A104207 A107646 A204607

Adjacent sequences: A083952 A083953 A083954 * A083956 A083957 A083958

Keyword

nonn

Author

Klaus Brockhaus, May 09 2003

Status

approved