

A160053


Numbers k with property that k*(k+1)/2 is sum of two nonnegative squares.


2



0, 1, 4, 8, 9, 16, 17, 25, 36, 40, 49, 52, 64, 72, 73, 80, 81, 89, 97, 100, 116, 121, 136, 144, 145, 148, 169, 180, 193, 196, 225, 232, 233, 241, 244, 256, 260, 288, 289, 292, 305, 313, 324, 337, 360, 361, 369, 388, 400, 404, 409, 424, 441, 449, 457, 481, 484
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OFFSET

1,3


COMMENTS

A000217(n) is term in A001481 and in A073613.
a(n) = A140612(n1) follows easily from the "sum of two squares theorem": x is the sum of two (nonnegative) squares iff its prime factorization does not contain p^e where p == 3 (mod 4) and e is odd.  Robert Israel, Mar 26 2018


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


MATHEMATICA

(*M6*) A1 = {}; Do[If[SquaresR[2, n (n + 1)/2] > 0, AppendTo[A1, n]], {n, 0, 1500}]; A1
Join[{0}, Flatten[Position[Accumulate[Range[500]], _?(SquaresR[2, #]> 0&)]]] (* Harvey P. Dale, Jun 07 2015 *)


CROSSREFS

Cf. A140612, A000217, A000404, A001481, A073613.
Sequence in context: A106840 A242663 A140612 * A225353 A034023 A086368
Adjacent sequences: A160050 A160051 A160052 * A160054 A160055 A160056


KEYWORD

nonn


AUTHOR

Zak Seidov, May 01 2009


STATUS

approved



