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

1,2

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A014117, A031971, A228869, A228870.

Sequence in context: A071703 A010069 A360912 * A132895 A125499 A240092

Adjacent sequences: A226869 A226870 A226871 * A226873 A226874 A226875

Keyword

nonn

Author

José María Grau Ribas, Jun 20 2013

Status

approved