A228869 -id:A228869 - cp's OEIS frontend

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

José María Grau Ribas, Jun 20 2013

nonn

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

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

Cf. A014117, A031971, A228869, A228870.

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

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

A228870 Numbers n such that 2 * (1^n + 2^n + 3^n + ... + n^n) is not 0 (mod n).

Original entry on oeis.org

6, 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 60, 66, 72, 78, 80, 84, 90, 96, 100, 102, 108, 110, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 180, 186, 192, 198, 200, 204, 210, 216, 220, 222, 228, 234, 240, 246, 252, 258, 260, 264, 270, 272

Offset: 1

T. D. Noe, Sep 06 2013

nonn

These are the numbers not appearing in A228869; the even numbers not in A226872.
Also, positive integers n such that there exists an odd prime divisor p of n such that (p-1) also divides n (cf. A124240). - Max Alekseyev, Sep 07 2013
This sequence agrees with A088723 for many terms, but they are different.
If n is in the sequence, then so are the multiples of n. See A280187 for primitive members of this sequence. - Charles R Greathouse IV, Dec 28 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A228869, A226872.

Select[Range[100], Mod[2*Sum[PowerMod[k, #, #], {k, #}], #] > 0 &]

is(n)=my(f=factor(n)[,1]); for(i=1,#f, if(n%(f[i]-1)==0 && f[i]>2, return(1))); 0 \\ Charles R Greathouse IV, Dec 28 2016

cp's OEIS Frontend

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

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