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 A055030 (Sum(m^(p-1),m=1..p-1)+1)/p as p runs through the primes. 7
 1, 2, 71, 9596, 1355849266, 1032458258547, 1653031004194447737, 3167496749732497119310, 22841077183004879532481321652, 1768861419039838982256898243427529138091, 10293527624511391856267274608237685758691696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It is conjectured that (Sum(m^(n-1),m=1..n-1)+1)/n is an integer iff n is 1 or a prime. Always an integer from little Fermat theorem. Converse is conjectured to be true: if p | (1+1^(p-1)+2^(p-1)+3^(p-1)+...+(p-1)^(p-1)) and p > 1, then p is prime. That was checked by Giuga up to p <= 10^1000. [Benoit Cloitre, Jun 09 2002] REFERENCES R. K. Guy, Unsolved Problems in Number Theory, A17. LINKS K. MacMillan and J. Sondow, Proofs of power sum and binomial coefficient congruences via Pascal's identity, Amer. Math. Monthly, 118 (2011), 549-551. PROG (PARI) for(n=1, 20, print1((1+sum(i=1, prime(n)-1, i^(prime(n)-1)))/prime(n), ", ")) /* Benoit Cloitre, Jun 09 2002*/ CROSSREFS Cf. A055031, A055032, A055023, A201560, A204187. Sequence in context: A221959 A221553 A071871 * A185120 A217842 A053318 Adjacent sequences:  A055027 A055028 A055029 * A055031 A055032 A055033 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 11 2000 EXTENSIONS Comments corrected by Jonathan Sondow, Jan 11 2012 STATUS approved

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