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A174050 Primes of the form x^2 + y^2 such that L(x)* L(y) = 1, where L is the Liouville lambda-function A008836. 1
2, 13, 17, 29, 37, 53, 73, 89, 97, 101, 113, 173, 181, 193, 197, 233, 241, 257, 277, 293, 313, 337, 349, 353, 373, 409, 421, 433, 449, 457, 521, 541, 569, 577, 593, 613, 641, 661, 673, 677, 709, 733, 757, 761, 809, 821, 853, 881, 929, 1021, 1033, 1049, 1069 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

One contribution to the set of solutions is from (x,y) where x and y are both prime, see A045637.

Another set of solutions is contributed if (x,y) are both in A026424.

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

2 is in the sequence because 2 = 1 + 1 and L(1)*L(1)= (1) *(1) = 1.

13 is in the sequence because 13 = 2^2 + 3^2 and L(2)*L(3)= (-1)*(-1) = 1.

193 is in the sequence because 193 = 12^2 + 7^2 and L(12)*L(7)= (-1)*(-1) = 1.

MAPLE

isA174050 := 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 1100 do

        if isA174050(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[200], Or @@ lambdaQ /@ PowersRepresentations[#, 2, 2] &] (* Jean-Fran├žois Alcover, Jul 30 2013 *)

CROSSREFS

Cf. A002819, A002313, A174054.

Sequence in context: A018459 A037384 A177964 * A122487 A109181 A175448

Adjacent sequences:  A174047 A174048 A174049 * A174051 A174052 A174053

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 06 2010

STATUS

approved

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Last modified May 31 00:29 EDT 2020. Contains 334747 sequences. (Running on oeis4.)