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 A118882 Numbers which are the sum of two squares in two or more different ways. 12
 25, 50, 65, 85, 100, 125, 130, 145, 169, 170, 185, 200, 205, 221, 225, 250, 260, 265, 289, 290, 305, 325, 338, 340, 365, 370, 377, 400, 410, 425, 442, 445, 450, 481, 485, 493, 500, 505, 520, 530, 533, 545, 565, 578, 580, 585, 610, 625, 629, 650, 676, 680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS E.g. squares of distances that are the distance between two points in the square lattice in two or more nontrivially different ways. A quadrilateral with sides a,b,c,d has perpendicular diagonals iff a^2+c^2 = b^2+d^2. This sequence is the sums of the squares of opposite sides of such quadrilaterals, excluding kites (a=b,c=d), but including right triangles (the degenerate case d=0). A000161(a(n)) > 1. [Reinhard Zumkeller, Aug 16 2011] LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA Numbers whose prime factorization includes at least two primes (not necessarily distinct) congruent to 1 mod 4 and any prime factor congruent to 3 mod 4 has even multiplicity. Products of two values in A004431. EXAMPLE 50 = 7^2 + 1^2 = 5^2 + 5^2, so 50 is in the sequence. MATHEMATICA Select[Range[1000], Length[PowersRepresentations[#, 2, 2]] > 1&] (* Jean-François Alcover, Mar 02 2019 *) PROG (Haskell) import Data.List (findIndices) a118882 n = a118882_list !! (n-1) a118882_list = findIndices (> 1) a000161_list -- Reinhard Zumkeller, Aug 16 2011 CROSSREFS Cf. A004431, A009177, A085265. Cf. A007692, A001481, A022544. Sequence in context: A236834 A033902 A009177 * A085625 A116490 A230213 Adjacent sequences:  A118879 A118880 A118881 * A118883 A118884 A118885 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, May 03 2006 STATUS approved

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Last modified January 17 23:59 EST 2021. Contains 340249 sequences. (Running on oeis4.)