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%I #56 May 09 2022 15:23:26
%S 0,3,26,255,3124,46655,823542,16777215,387420488,9999999999,
%T 285311670610,8916100448255,302875106592252,11112006825558015,
%U 437893890380859374,18446744073709551615,827240261886336764176,39346408075296537575423,1978419655660313589123978
%N a(n) = n^n - 1.
%C From _Alexander Adamchuk_, Jan 22 2007: (Start)
%C a(n) is divisible by (n-1).
%C Corresponding quotients are a(n)/(n-1) = {1,3,13,85,781,9331, ...} = A023037(n).
%C p divides a(p-1) for prime p.
%C 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.
%C 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.
%C 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.
%C p divides a((p-1)/5) for prime p = {31,191,251,271,601,641,761,1091,...}.
%C p divides a((p-1)/6) for prime p = {7,241,313,337,409,439,607,631,727,751,919,937,...}. (End)
%C For n > 1, a(n) is largest number that can be represented using n digits in the base-n number system. - _Chinmaya Dash_, Mar 31 2022
%D 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.
%H G. C. Greubel, <a href="/A048861/b048861.txt">Table of n, a(n) for n = 1..385</a>
%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>
%F E.g.f.: 1/(1+LambertW(-x)) - exp(x). - _Vaclav Kotesovec_, Dec 20 2014
%e For n=3, a(n) = 3^3 - 1 = 27 - 1 = 26. - _Michael B. Porter_, Nov 12 2017
%t Table[n^n - 1, {n, 1, 50}] (* _G. C. Greubel_, Nov 10 2017 *)
%o (Magma) [ n^n-1: n in [1..25]]; // _Vincenzo Librandi_, Dec 29 2010
%o (PARI) a(n)=n^n-1 \\ _Charles R Greathouse IV_, Feb 24 2012
%Y Cf. A000312, A048860, A023037, A033200, A014753, A002144.
%K nonn,easy
%O 1,2
%A Charles T. Le (charlestle(AT)yahoo.com)
%E Extended (and corrected) by _Patrick De Geest_, Jul 15 1999
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