A226872 1 together with even numbers n >= 2 such that 1^n + 2^n + 3^n + ... + n^n == n/2 (mod n).

1, 2, 4, 8, 10, 14, 16, 22, 26, 28, 32, 34, 38, 44, 46, 50, 52, 56, 58, 62, 64, 68, 70, 74, 76, 82, 86, 88, 92, 94, 98, 104, 106, 112, 116, 118, 122, 124, 128, 130, 134, 136, 142, 146, 148, 152, 154, 158, 164, 166, 170, 172, 176, 178, 182, 184, 188, 190, 194, 196

Offset: 1

Author

José María Grau Ribas, Jun 20 2013

Keywords

• nonn

Comments

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014117, A031971, A228869, A228870.

Programs

Mathematica

Join[{1}, Select[Range[200], Mod[Sum[PowerMod[k, #, #], {k, #}], #] == #/2 &]] (* T. D. Noe, Sep 04 2013 *)

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