A084349 Squarefree numbers that are not the sum of two squares.

1, 3, 6, 7, 11, 14, 15, 19, 21, 22, 23, 30, 31, 33, 35, 38, 39, 42, 43, 46, 47, 51, 55, 57, 59, 62, 66, 67, 69, 70, 71, 77, 78, 79, 83, 86, 87, 91, 93, 94, 95, 102, 103, 105, 107, 110, 111, 114, 115, 118, 119, 123, 127, 129, 131, 133, 134, 138, 139, 141, 142, 143

Offset: 1

Author

Reinhard Zumkeller, Jun 21 2003

Keywords

• nonn

Comments

Intersection of A005117 (squarefree) and A018825. - Michel Marcus, Dec 02 2015

Examples

			A005117(10) = 14: 14 - 1^2 = 13, 14 - 2^2 = 10 and 14 - 3^3 = 5 are nonsquares, therefore 14 is a term;
A005117(9) = 13 is not a term: A020893(4) = 13 = 2^2 + 3^2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000290, A005117, A010052, A018825, A020893.

Programs

Haskell

a084349 n = a084349_list !! (n-1)
a084349_list = 1 : filter (\x -> all (== 0) $ map (a010052 . (x -)) $
                           takeWhile (<= x) a000290_list) a005117_list
-- Reinhard Zumkeller, Dec 11 2011

Mathematica

Prepend[Select[Range@ 144, SquareFreeQ@ # && SquaresR[2, #] == 0 &], 1] (* Michael De Vlieger, Dec 02 2015 *)