cp's OEIS Frontend

A085606 a(n) = (n-1)^n - 1.

%I A085606 #16 May 31 2022 06:47:49
%S A085606 0,-1,0,7,80,1023,15624,279935,5764800,134217727,3486784400,
%T A085606 99999999999,3138428376720,106993205379071,3937376385699288,
%U A085606 155568095557812223,6568408355712890624,295147905179352825855,14063084452067724991008,708235345355337676357631
%N A085606 a(n) = (n-1)^n - 1.
%C A085606 Sequence relates to the "monkey and coconut problem"(A014293) giving the number of coconuts received by each of the n sailors from the ultimate equitable distribution the next day.
%C A085606 From _Alexander Adamchuk_, Nov 13 2006: (Start)
%C A085606 4n^2 divides a(2n).
%C A085606 Odd prime p divides a(p-1).
%C A085606 8p^2 divides a(2p) for an odd prime p.
%C A085606 32p^4 divides a(2p^2) for an odd prime p.
%C A085606 64p^8 divides a(2p^4) for an odd prime p.
%C A085606 p^3 divides a(p^3+2) for prime p.
%C A085606 p divides a((p-1)/2) for prime p in A157437.
%C A085606 p^2 divides a((p-1)/2) for prime p = {5,127,607}. (End)
%F A085606 a(n) = A065440(n) - 1.
%t A085606 Table[(n-1)^n-1,{n,0,30}] (* _Alexander Adamchuk_, Nov 13 2006 *)
%Y A085606 Cf. A014293, A007778, A065440, A037205, A157437.
%K A085606 sign
%O A085606 0,4
%A A085606 _Lekraj Beedassy_, Jul 07 2003
%E A085606 More terms from _Ray Chandler_, Nov 10 2003