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A118882 Numbers which are the sum of two squares in two or more different ways. 11
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

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.

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 August 21 13:21 EDT 2017. Contains 290890 sequences.