A046730 a(n) = A002172(n) / 2.

-1, 3, 1, -5, -1, 5, 7, -5, -3, 5, 9, -1, 3, -7, -11, 7, 11, -13, -9, -7, -1, 15, 13, -15, 1, -13, -9, 5, -17, 13, 11, 9, -5, 17, 7, -17, 19, 1, -3, 15, 17, -7, 21, 19, -5, -11, -21, 19, 13, 1, -23, 5, -17, -19, 25, -13, -25, -23, -1, -5, 15, 27, -9, -19, 25, -17, 11, 5, -25, 27, 23, 29, -29, 25

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

L. Carlitz, The coefficients of the lemniscate function, Math. Comp., 16 (1962), 475-478.

Index entries for sequences related to Glaisher's numbers

Example

From Seiichi Manyama, Sep 26 2016: (Start)
Let p be a prime of the form 4k+1 so that p = a^2 + b^2.
We take a odd and such that a = b + 1 (mod 4).
p =  5 = (-1)^2 + 2^2 and -1 = 2 + 1 (mod 4). So a(1) = -1.
p = 13 =    3^2 + 2^2 and  3 = 2 + 1 (mod 4). So a(2) =  3.
p = 17 =    1^2 + 4^2 and  1 = 4 + 1 (mod 4). So a(3) =  1.
p = 29 =    5^2 + 2^2 and -5 = 2 + 1 (mod 4). So a(4) = -5.
(End)

Mathematica

Map[-Sum[JacobiSymbol[x^3 - x, #], {x, 0, # - 1}] &, Select[Prime@ Range@ 155, Mod[#, 4] == 1 &]]/2 (* Michael De Vlieger, Sep 26 2016, after Jean-François Alcover at A002172 *)

Prog

(PARI) a002172(n) = {my(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)))}
a(n) = a002172(n)/2; \\ Altug Alkan, Sep 27 2016

Crossrefs

Cf. A002172.

Sequence in context: A214737 A348161 A334194 * A002972 A324896 A029652

Adjacent sequences: A046727 A046728 A046729 * A046731 A046732 A046733

Keyword

sign

Author

N. J. A. Sloane

Extensions

Offset changed to 1 to match A002172, Joerg Arndt, Sep 27 2016

Status

approved