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A073613 Triangular numbers which are the sum of two squares. 2
0, 1, 10, 36, 45, 136, 153, 325, 666, 820, 1225, 1378, 2080, 2628, 2701, 3240, 3321, 4005, 4753, 5050, 6786, 7381, 9316, 10440, 10585, 11026, 14365, 16290, 18721, 19306, 25425, 27028, 27261, 29161, 29890, 32896, 33930, 41616, 41905, 42778 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The squares may be zero.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

Intersection of A000217 and A001481.

EXAMPLE

0 = A000217(0) = A001481(1) = 0^2 + 0^2 is listed here as a(1).

1 = A000217(1) = A001481(2) = 1^2 + 0^2 is listed here as a(2).

10 = A000217(4) = A001481(8) = 1^2 + 9^2 is listed here as a(3).

MAPLE

filter:= proc(n)

  andmap(t -> (t[1] mod 4 <> 3 or t[2]::even), ifactors(n)[2])

end proc:

select(filter, [seq(i*(i+1)/2, i=0..500)]); # Robert Israel, Nov 22 2017

MATHEMATICA

t = Range[0, 250]^2; t1 = Flatten[Table[a + b, {a, t}, {b, t}]]; t2 = Accumulate[Range[300]]; Intersection[t1, t2] (* Jayanta Basu, Jul 03 2013 *)

Select[Union[Total/@Tuples[Range[0, 300]^2, 2]], OddQ[Sqrt[8#+1]]&] (* Harvey P. Dale, Apr 22 2015 *)

PROG

(PARI) is_A073613(n)=is_A000217(n)&&is_A001481(n) \\ M. F. Hasler, Nov 20 2017

CROSSREFS

Cf. A000217 (triangular numbers), A001481 (sums of two squares).

Sequence in context: A125550 A223305 A176575 * A117404 A072517 A271912

Adjacent sequences:  A073610 A073611 A073612 * A073614 A073615 A073616

KEYWORD

easy,nonn

AUTHOR

Jason Earls, Aug 29 2002

EXTENSIONS

Edited and initial 0 added by M. F. Hasler, Nov 20 2017

STATUS

approved

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Last modified February 22 14:10 EST 2018. Contains 299454 sequences. (Running on oeis4.)