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 A002172 Glaisher's chi numbers chi(p) for p a prime of the form 4m+1. (Formerly M1556 N0607) 6

%I M1556 N0607

%S -2,6,2,-10,-2,10,14,-10,-6,10,18,-2,6,-14,-22,14,22,-26,-18,-14,-2,

%T 30,26,-30,2,-26,-18,10,-34,26,22,18,-10,34,14,-34,38,2,-6,30,34,-14,

%U 42,38,-10,-22,-42,38,26,2,-46,10,-34,-38,50,-26,-50,-46,-2,-10,30,54,-18,-38,50,-34,22,10,-50,54,46,58,-58,50

%N Glaisher's chi numbers chi(p) for p a prime of the form 4m+1.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A002172/b002172.txt">Table of n, a(n) for n = 1..1000</a>

%H J. W. L. Glaisher, <a href="http://gdz.sub.uni-goettingen.de/en/dms/loader/img/?PPN=PPN600494829_0020&amp;DMDID=DMDLOG_0012">On the function chi(n)</a>, Quarterly Journal of Pure and Applied Mathematics, 20 (1884), 97-167.

%H J. W. L. Glaisher, <a href="/A002171/a002171.pdf">On the function chi(n)</a>, Quarterly Journal of Pure and Applied Mathematics, 20 (1884), 97-167. [Annotated scanned copy]

%H <a href="/index/Ge#Glaisher">Index entries for sequences related to Glaisher's numbers</a>

%t pp = Select[ Prime[ Range[200]], Mod[#, 4] == 1 & ]; (-Sum[ JacobiSymbol[x^3 - x, #], {x, 0, # - 1}] & ) /@ pp (* _Jean-François Alcover_, Oct 07 2011, after _Michael Somos_ *)

%o (PARI) {a(n)= local(m, c); if(n<1, 0, c=0; m=0; while(c<n, m++; if(isprime(m)& m%4==1, c++)); -sum(x=0, m-1, kronecker(x^3-x, m)))} /* _Michael Somos_, Sep 19 2006 */

%Y Cf. A002171.

%K nice,sign

%O 1,1

%A _N. J. A. Sloane_

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Last modified October 23 10:00 EDT 2019. Contains 328345 sequences. (Running on oeis4.)