1,2

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 (alex(AT)kolmogorov.com), Jan 22 2007

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.

F. Smarandache, Only Problems, Not Solutions!, Xiquan Publ. Hse., 1990, Problem 17.

M. L. Perez et al., eds., Smarandache Notions Journal

F. Smarandache, Only Problems, Not Solutions!

a[n_]:=n^n-1; lst={}; Do[AppendTo[lst, a[n]], {n, 1, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]

Cf. A000312, A048860.

Cf. A023037, A033200, A014753, A002144.

Sequence in context: A067858 A052141 A062793 this_sequence A053972 A126738 A109074

Adjacent sequences: A048858 A048859 A048860 this_sequence A048862 A048863 A048864

nonn,easy

Charles T. Le (charlestle(AT)yahoo.com)

Extended (and corrected) by Patrick De Geest (pdg(AT)worldofnumbers.com), 7/99.