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%I #49 Sep 06 2013 12:22:05
%S 1,2,4,8,10,14,16,22,26,28,32,34,38,44,46,50,52,56,58,62,64,68,70,74,
%T 76,82,86,88,92,94,98,104,106,112,116,118,122,124,128,130,134,136,142,
%U 146,148,152,154,158,164,166,170,172,176,178,182,184,188,190,194,196
%N 1 together with even numbers n >= 2 such that 1^n + 2^n + 3^n + ... + n^n == n/2 (mod n).
%C For n>1, a(n) is even. Alternatively, the even terms of this sequence can be characterized in any of the following ways: (i) even integers n such that n*B(n) == n/2 (mod n), where B(n) is the n-th Bernulli number; OR (ii) integers n such that gcd(n,A027642(n)) = 2; OR (iii) even integers n such that (p-1) does not divide n for every odd prime p dividing n (cf. A124240). - _Max Alekseyev_, Sep 05 2013
%H Charles R Greathouse IV, <a href="/A226872/b226872.txt">Table of n, a(n) for n = 1..10000</a>
%t Join[{1}, Select[Range[200], Mod[Sum[PowerMod[k, #, #], {k, #}], #] == #/2 &]] (* _T. D. Noe_, Sep 04 2013 *)
%o (PARI) is(n)=if(n%2,return(n==1));my(f=factor(n)[,1]);for(i=2,#f,if(n%(f[i]-1)==0,return(0)));1 \\ _Charles R Greathouse IV_, Sep 04 2013
%Y Cf. A014117, A031971, A228869, A228870.
%K nonn
%O 1,2
%A _José María Grau Ribas_, Jun 20 2013