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 A174054 Primes of the form x^2+y^2 such that L(x)*L(y) = -1, where L) is the Liouville lambda-function A008836. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE 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 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 *) CROSSREFS Cf. A174050, A002313. Sequence in context: A041599 A302692 A232881 * A106963 A276916 A203018 Adjacent sequences:  A174051 A174052 A174053 * A174055 A174056 A174057 KEYWORD nonn AUTHOR Michel Lagneau, Mar 06 2010 STATUS approved

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Last modified May 29 10:41 EDT 2020. Contains 334699 sequences. (Running on oeis4.)