

A088790


Numbers n such that (n^n1)/(n1) is prime.


8




OFFSET

1,1


COMMENTS

Note that (n^n1)/(n1) is prime only if n is prime, in which case it equals cyclotomic(n,n), the nth cyclotomic polynomial evaluated at x=n. This sequence is a subset of A070519. The number cyclotomic(7547,7547) is a probable prime found by H. Lifchitz. Are there only a finite number of these primes?
Contribution from T. D. Noe, Dec 16 2008: (Start)
The standard heuristic implies that there are an infinite number of these primes and that the next n should be between 10^10 and 10^11.
Let N = (7547^75471)/(75471) = A023037(7547). If N is prime, then the period of the Bell numbers modulo 7547 is N. See A054767. (End)


REFERENCES

R. K. Guy, Unsolved Problems in Theory of Numbers, 1994, A3.


LINKS

Table of n, a(n) for n=1..5.
Bernard Schott, Les nombres brĂ©siliens, Quadrature, no. 76, avriljuin 2010, pages 3038; included here with permission from the editors of Quadrature.
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial


MATHEMATICA

Do[p=Prime[n]; If[PrimeQ[(p^p1)/(p1)], Print[p]], {n, 100}]


PROG

(PARI) is(n)=ispseudoprime((n^n1)/(n1)) \\ Charles R Greathouse IV, Feb 17 2017


CROSSREFS

Cf. A070519 (cyclotomic(n, n) is prime).
Cf. A056826 ((n^n+1)/(n+1) is prime).
Sequence in context: A040145 A142955 A213896 * A283186 A215304 A215281
Adjacent sequences: A088787 A088788 A088789 * A088791 A088792 A088793


KEYWORD

hard,more,nonn


AUTHOR

T. D. Noe, Oct 16 2003


STATUS

approved



