

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
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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
Index entries for sequences related to sums of squares


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&] (* JeanFrançois Alcover, Mar 02 2019 *)


PROG

(Haskell)
import Data.List (findIndices)
a118882 n = a118882_list !! (n1)
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. AdamsWatters, May 03 2006


STATUS

approved



