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A102327 Primes p such that the largest prime factor of p^5 + 1 is less than p. 0
1753, 2357, 7103, 9749, 13441, 16453, 21467, 22739, 25153, 28409, 29059, 33247, 33347, 36781, 42853, 51427, 57751, 58453, 62347, 65777, 66593, 69119, 72923, 78643, 80407, 83591, 85619, 89909, 91411, 99409, 101209, 101363, 113171, 124337 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..34.

FORMULA

Solutions to {A006530(1 + p^5) < p} where p is a prime.

EXAMPLE

p = 1753, 1 + p^5 = 16554252702583994 = 2*41*151*691*877*1361*1621, so the largest prime factor is 1621 < p = 1753.

MATHEMATICA

<<NumberTheory`NumberTheoryFunctions` Select[Prime[Range[15000]], Max[PrimeFactorList[1 + #^5]] < # &] (* Ray Chandler, Jan 08 2005 *)

Select[Prime[Range[12000]], FactorInteger[#^5+1][[-1, 1]]<#&]  (* Harvey P. Dale, Mar 14 2011 *)

PROG

(PARI) isok(p)= isprime(p) && (vecmax(factor(p^5+1)[, 1]) < p); \\ Michel Marcus, Jul 11 2018

CROSSREFS

Cf. A000040, A065091, A073501.

Sequence in context: A143994 A157325 A223448 * A076809 A272326 A271747

Adjacent sequences:  A102324 A102325 A102326 * A102328 A102329 A102330

KEYWORD

nonn

AUTHOR

Labos Elemer, Jan 05 2005

EXTENSIONS

Extended by Ray Chandler, Jan 08 2005

STATUS

approved

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Last modified November 26 03:20 EST 2020. Contains 338632 sequences. (Running on oeis4.)