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 A195812 Sum of the distinct residues of x^n (mod n), x=0..n-1. 3
 0, 1, 3, 1, 10, 8, 21, 1, 9, 25, 55, 14, 78, 42, 105, 1, 136, 20, 171, 22, 84, 110, 253, 26, 50, 169, 27, 84, 406, 150, 465, 1, 528, 289, 595, 38, 666, 342, 273, 42, 820, 130, 903, 198, 315, 460, 1081, 50, 147, 125, 1275, 156, 1378, 56, 385, 140, 570, 841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) has the following properties : If n is a power of 2 then a(n)= 1 ; Except for n = 9 where a(9)=9, if a(n) is the square of a prime p, the sequence shows that n is of the form n = 2p. The numbers m such that a(m) are square are : 1, 2, 4, 8, 9, 10, 16, 26, 32, 34, 58, 64, 74, 81, ... LINKS Zak Seidov, Table of n, a(n) for n = 1..1000 EXAMPLE a(10) = 25 because the residues (mod 10) of x^10 are 0, 1, 4, 5, 6, 9 and the sum 25 is a square => a(10) = a(2*5)= 5^2. 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           printf("%d, ", sumDistRes(n)); end do: # (Program of R. J. Mathar - see A196546) MATHEMATICA Table[{m, Total[Union[Table[PowerMod[x, m, m], {x, m-1}]]]}, {m, 1000}] (* Zak Seidov, Oct 06 2011 *) PROG (PARI) a(n) = vecsum(Set(vector(n, k, lift(Mod(k-1, n)^n)))); \\ Michel Marcus, Jun 01 2015 CROSSREFS Cf. A196546, A196547. Sequence in context: A084178 A262030 A260178 * A264491 A144697 A185419 Adjacent sequences:  A195809 A195810 A195811 * A195813 A195814 A195815 KEYWORD nonn AUTHOR Michel Lagneau, Oct 05 2011 STATUS approved

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Last modified January 21 02:59 EST 2019. Contains 319344 sequences. (Running on oeis4.)