|
| |
|
|
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; 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
| Index entries for sequences related to sums of squares
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.
|
|
|
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: A040600 A033902 A009177 * A085625 A116490 A008607
Adjacent sequences: A118879 A118880 A118881 * A118883 A118884 A118885
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), May 03 2006
|
| |
|
|
