login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A196546 Numbers n such that the sum of the distinct residues of x^n (mod n), x=0..n-1, is divisible by n. 4
1, 3, 5, 7, 9, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 33, 35, 37, 38, 39, 41, 43, 45, 46, 47, 49, 51, 52, 53, 55, 57, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 75, 77, 78, 79, 81, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 98, 99, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All odd prime numbers are in the sequence.

The sum of the distinct residues is 0, 1, 3, 1, 10, 8, 21, 1, 9, 25, 55, 14, 78, 42, 105, 1, 136,.. for n>=1.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

n= 14 is in the sequence because x^14 == 0, 1, 2, 4, 7, 8, 9, or 11 (mod 14), and the sum  0+1+2+4+7+8+9+11 = 42 is divisible by 14.

MAPLE

sumDistRes := proc(n)

        local re, x, r ;

        re := {} ;

        for x from 0 to n-1 do

                re := re union { modp(x^n, n) } ;

        end do:

        add(r, r=re) ;

end proc:

for n from 1 to 100 do

        if sumDistRes(n) mod n = 0 then

                printf("%d, ", n);

        end if;

end do: # R. J. Mathar, Oct 04 2011

CROSSREFS

Cf. A195637.

Sequence in context: A081534 A214547 A097218 * A231773 A007617 A065878

Adjacent sequences:  A196543 A196544 A196545 * A196547 A196548 A196549

KEYWORD

nonn

AUTHOR

Michel Lagneau, Oct 03 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 25 03:30 EDT 2021. Contains 345449 sequences. (Running on oeis4.)