%I A123570
%S A123570 1,2,9,82,1025,15626,279937,5764802,134217729,3486784402,100000000001,
%T A123570 3138428376722,106993205379073,3937376385699290,155568095557812225,
%U A123570 6568408355712890626,295147905179352825857,14063084452067724991010
%N A123570 n^(n+1) + 1.
%C A123570 (2n+1)^2 divides a(2n). a(2n)/(2n+1)^2 = {1,1,41,5713,1657009,826446281,
               633095889817,691413758034721,...} = A081215(2n). p divides a(p-1) 
               for prime p. a(p-1)/p = {1,3,205,39991,9090909091,8230246567621,...} 
               = A081209(p-1) = A076951(p-1). p^2 divides a(p-1) for an odd prime 
               p. a(p-1)/p^2 = {1,41,5713,826446281,633095889817,1021273028302258913,
               1961870762757168078553, 14199269001914612973017444081,...} = A081215(p-1). 
               Prime p divides a((p-3)/2) for p = {13,17,19,23,37,41,43,47,61,67,
               71,89,109,113,137,139,157,163,167,181,191,...}. Prime p divides a((p-5)/
               4) for p = {29,41,61,89,229,241,281,349,421,509,601,641,661,701,709,
               769,809,821,881,...} = A107218(n) Primes of the form 4x^2+25y^2. 
               Prime p divides a((p-7)/6) for p = {79,109,127,151,313,421,541,601,
               613,751,757,787,...}. Prime p divides a((p-9)/8) for p = {41,337,
               401,521,569,577,601,857,929,937,953,977,...} A subset of A007519(n) 
               Primes of form 8n+1. Prime p divides a((p-11)/10) for p = {41,181,
               331,601,761,1021,1151,1231,1801,...}. Prime p divides a((p-13)/12) 
               for p = {313,337,433,1621,1873,1993,2161,2677,2833,...}.
%F A123570 a(n) = n^(n+1) + 1. a(n) = A007778(n) + 1.
%t A123570 Table[n^(n+1)+1,{n,0,30}]
%Y A123570 Cf. A007778 - n^(n+1). Cf. A000312 - n^n. Cf. A014566 - Sierpinski numbers 
               of the first kind: n^n + 1. Cf. A081209, A076951, A081215.
%Y A123570 Sequence in context: A147302 A112670 A117581 this_sequence A006040 A067309 
               A087798
%Y A123570 Adjacent sequences: A123567 A123568 A123569 this_sequence A123571 A123572 
               A123573
%K A123570 nonn
%O A123570 0,2
%A A123570 Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 12 2006