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A124239 a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k - 1)^m. 3

%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*k-1) 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[(2k-1)^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

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Last modified June 14 01:29 EDT 2021. Contains 345016 sequences. (Running on oeis4.)