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A196730 Numbers m such that the sum of the distinct residues of x^m (mod m) is a perfect square, x=0..m-1. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 05:24 EDT 2020. Contains 334649 sequences. (Running on oeis4.)