%I
%S 1,14,197,3704,90309,2704470,95856025,3921108576,181756280697,
%T 9413656622446,538727822713277,33757715581666296,2298714540642445405,
%U 169016703698449309846,13345320616706684277361
%N a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k  1)^m.
%C a(3) = 197 and a(11) = 538727822713277 are primes. p divides a(p+1) for primes p > 3. a(2*k1) is odd. a(2*k) is even. a(2^k) is divisible by 2^(2*k  1) for k > 0.
%C Numbers n such that a(n) is divisible by n (1, 2, 4, 6, 8, 12, ...) are listed in A124240(n).
%C It appears that A124240(n) almost coincides with A068563(n) (numbers n such that 2^n (mod n) = 4^n (mod n)). The first term that is different is A068563(27) = 136. The terms of A068563(n) that are not the terms of A124240(n) (136, 408, 620, 680, 820, ...) are listed in A124241(n).
%H T. D. Noe, <a href="/A124239/b124239.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k  1)^m.
%F a(n) = n + Sum_{k=2..n} (2*k  1)*((2*k  1)^n  1)/(2*(k  1)).
%t Table[Sum[(2k1)^m,{k,1,n},{m,1,n}],{n,1,20}]
%Y Cf. A124240, A124241.
%Y Cf. also A068563, A086787, A123855.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, Oct 22 2006
