A174054 Primes of the form x^2+y^2 such that L(x)*L(y) = -1, where L is the Liouville lambda-function A008836.

5, 41, 61, 109, 137, 149, 157, 229, 269, 281, 317, 389, 397, 401, 461, 509, 557, 601, 617, 653, 701, 769, 773, 797, 829, 857, 877, 937, 941, 977, 997, 1009, 1013, 1061, 1093, 1097, 1153, 1181, 1213, 1217, 1229, 1249, 1277, 1289, 1321, 1409, 1453, 1489

Offset: 1

Author

Michel Lagneau, Mar 06 2010

Keywords

• nonn

Examples

			5 = 1 + 2^2 and L(1)*L(2)= (1) *(-1) = -1.
41 = 4^2 + 5^2 and L(4)*L(5)= (1)*(-1) = -1
		

Crossrefs

Cf. A174050, A002313.

Programs

Maple

isA174054 := proc(n)
        local x,y ;
        if not isprime(n) then
                return false;
        end if;
        for x from 1 do
                if x^2 > n then
                        return false;
                end if;
                if issqr(n-x^2) then
                        y := sqrt(n-x^2) ;
                        if A008836(x) * A008836(y) = -1 then
                                return true;
                        end if;
                end if;
        end do:
end proc:
for n from 1 to 2000 do
        if isA174054(n) then
                printf("%d,\n",n) ;
        end if;
end do: # R. J. Mathar, Jul 09 2012

Mathematica

lambdaQ[{x_, y_}] := LiouvilleLambda[x]*LiouvilleLambda[y] == -1; Select[ Prime /@ Range[300], Or @@ lambdaQ /@ PowersRepresentations[#, 2, 2] &] (* Jean-François Alcover, Jul 30 2013 *)