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

-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

Author

N. J. A. Sloane

Keywords

• nice
• sign

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

Crossrefs

Cf. A002171.

Programs

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 *)

PARI

{a(n)= local(m, c); if(n<1, 0, c=0; m=0; while(cMichael Somos, Sep 19 2006 */