A048860 -id:A048860 - cp's OEIS frontend

A048861 a(n) = n^n - 1.

0, 3, 26, 255, 3124, 46655, 823542, 16777215, 387420488, 9999999999, 285311670610, 8916100448255, 302875106592252, 11112006825558015, 437893890380859374, 18446744073709551615, 827240261886336764176, 39346408075296537575423, 1978419655660313589123978

Offset: 1

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

From Alexander Adamchuk, Jan 22 2007: (Start)
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,...}. (End)
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

			For n=3, a(n) = 3^3 - 1 = 27 - 1 = 26. - _Michael B. Porter_, Nov 12 2017

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.

G. C. Greubel, Table of n, a(n) for n = 1..385
F. Smarandache, Only Problems, Not Solutions!

Cf. A000312, A048860, A023037, A033200, A014753, A002144.

[ n^n-1: n in [1..25]]; // Vincenzo Librandi, Dec 29 2010

Table[n^n - 1, {n, 1, 50}] (* G. C. Greubel, Nov 10 2017 *)

a(n)=n^n-1 \\ Charles R Greathouse IV, Feb 24 2012

E.g.f.: 1/(1+LambertW(-x)) - exp(x). - Vaclav Kotesovec, Dec 20 2014

Extended (and corrected) by Patrick De Geest, Jul 15 1999

A098853 Consider the smallest denominator q such that the Sylvester expansion of n/q has n terms. Here q has the form q = k*n+1 and we set a(n) = k.

Original entry on oeis.org

0, 1, 2, 4, 6, 18, 36, 12, 30, 162, 18, 330, 136, 858, 1092, 198, 1470, 882, 9520, 13260, 124800, 1216, 33966, 603060, 27742, 2141898, 677586

Offset: 1

Matthijs Coster, Oct 11 2004

			a(5)=6 because 5*6+1 = 31 and 5/31 = 1/7 + 1/55 + 1/3979 + 1/23744683 + 1/1127619917796295.

Matthijs Coster, Some sequences.

Cf. A048860.

a(n)=if(n==1,q=1,q=n+1;while(1,c=1;P=n;Q=q;while(Q%P>0,c++;D=Q\P+1;P=P*D-Q;Q*=D);if(c==n,break);q+=n));return((q-1)/n)

a(n) = (A048860(n)-1)/n.

Two more terms computed from A048860 by Max Alekseyev, Mar 08 2010

a(20)-a(27) from Robert Gerbicz, Nov 19 2010

cp's OEIS Frontend

A048861 a(n) = n^n - 1.

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