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 A048861 n^n-1. 9
 0, 3, 26, 255, 3124, 46655, 823542, 16777215, 387420488, 9999999999, 285311670610, 8916100448255, 302875106592252, 11112006825558015, 437893890380859374, 18446744073709551615, 827240261886336764176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is divisible by (n - 1). Corresponding quotients are a(n)/(n - 1) = {1, 3, 13, 85, 781, 9331, ...} = A023037(n). p divides a(p-1) for prime p. p divides a((p-1)/2) for prime p = {3,11,17,19,41,43,59,67,73,83,89,97,...} = A033200 Primes congruent to {1, 3} mod 8; or, odd primes of form x^2+2*y^2. p divides a((p-1)/3) for prime p = {61,67,73,103,151,193,271,307,367,...} = A014753 3 and -3 are both cubes (one implies other) mod these primes p=1 mod 6. p divides a((p-1)/4) for prime p = {5,13,17,29,37,41,53,61,73,...} = A002144 Pythagorean primes: primes of form 4n+1. p divides a((p-1)/5) for prime p = {31,191,251,271,601,641,761,1091,...}. p divides a((p-1)/6) for prime p = {7,241,313,337,409,439,607,631,727,751,919,937,...}. - Alexander Adamchuk, Jan 22 2007 REFERENCES M. Le, Primes in the sequences n^n+1 and n^n-1, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 156-157. LINKS F. Smarandache, Only Problems, Not Solutions! MATHEMATICA a[n_]:=n^n-1; lst={}; Do[AppendTo[lst, a[n]], {n, 1, 5!}]; lst [From Vladimir Joseph Stephan Orlovsky, Dec 11 2008] PROG (MAGMA)[ n^n-1: n in [1..25]]; [From Vincenzo Librandi, Dec 29 2010] (PARI) a(n)=n^n-1 \\ Charles R Greathouse IV, Feb 24 2012 CROSSREFS Cf. A000312, A048860, A023037, A033200, A014753, A002144. Sequence in context: A067858 A052141 A062793 * A053972 A204561 A126738 Adjacent sequences:  A048858 A048859 A048860 * A048862 A048863 A048864 KEYWORD nonn,easy,changed AUTHOR Charles T. Le (charlestle(AT)yahoo.com) EXTENSIONS Extended (and corrected) by Patrick De Geest, 7/99. STATUS approved

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