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

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

Offset

1,1

References

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

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

J. W. L. Glaisher, On the function chi(n), Quarterly Journal of Pure and Applied Mathematics, 20 (1884), 97-167.

J. W. L. Glaisher, On the function chi(n), Quarterly Journal of Pure and Applied Mathematics, 20 (1884), 97-167. [Annotated scanned copy]

Index entries for sequences related to Glaisher's numbers

Mathematica

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 *)

Prog

(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 */

Crossrefs

Cf. A002171.

Sequence in context: A369994 A199154 A267859 * A126289 A200044 A154382

Adjacent sequences: A002169 A002170 A002171 * A002173 A002174 A002175

Keyword

nice,sign

Author

N. J. A. Sloane

Status

approved