A196730 Numbers m such that the sum of the distinct residues of x^m (mod m) is a perfect square, x=0..m-1.

1, 2, 4, 8, 9, 10, 16, 26, 32, 34, 58, 64, 74, 81, 82, 84, 106, 122, 128, 146, 178, 194, 196, 202, 218, 226, 250, 256, 274, 298, 314, 346, 361, 362, 386, 394, 441, 458, 466, 480, 482, 512, 514, 538, 554, 562, 586, 626, 634, 674, 676, 698, 706, 722, 729, 746

Offset

1,2

Comments

m such that A195812(m) is a perfect square.

Links

Table of n, a(n) for n=1..56.

Example

a(8) = 26 because x^26 == > 0, 1, 3, 4, 9, 10, 12, 13, 14, 16, 17, 22, 23, 25  (mod 26), and the sum  = 169 = 13^2.

Maple

sumSquares := 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 750 do
z:= sqrt(sumSquares(n));
if z=floor(z) then
printf("%d, ", n);
end if;
end do: #

Crossrefs

Cf. A195812, A196547, A196546, A195637.

Sequence in context: A328945 A050907 A100675 * A325942 A325944 A165569

Adjacent sequences: A196727 A196728 A196729 * A196731 A196732 A196733

Keyword

nonn

Author

Michel Lagneau, Oct 05 2011

Status

approved