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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
OFFSET
1,2
COMMENTS
m such that A195812(m) is a perfect square.
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Oct 05 2011
STATUS
approved