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Search: id:A118882
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| A118882 |
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Numbers which are the sum of two squares in two or more different ways. |
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+0
7
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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).
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LINKS
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Index entries for sequences related to sums of squares
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FORMULA
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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.
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EXAMPLE
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50 = 7^2 + 1^2 = 5^2 + 5^2, so 50 is in the sequence.
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CROSSREFS
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Cf. A004431, A009177, A085265.
Sequence in context: A040600 A033902 A009177 this_sequence A085625 A116490 A008607
Adjacent sequences: A118879 A118880 A118881 this_sequence A118883 A118884 A118885
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KEYWORD
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nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 03 2006
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