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A224921 Number of Pythagorean triples (a, b, c) with a^2 + b^2 = c^2 and 0 < a < b < c < n. 8
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 8, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 13, 14, 14, 15, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 20, 21, 22, 23, 23, 24, 24, 24, 25, 25, 26, 27, 27, 27, 27, 31, 31, 31, 32, 32, 33, 33, 33 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

LINKS

Reiner Moewald and Robert Israel, Table of n, a(n) for n = 1..10000 (n=1..500 from Reiner Moewald)

MAPLE

a046080:= proc(n) local F, t;

  F:= select(t -> t[1] mod 4 = 1, ifactors(n)[2]);

  1/2*(mul(2*t[2]+1, t=F)-1)

end proc:

ListTools:-PartialSums(map(a046080, [$0..100])); # Robert Israel, Jul 18 2016

MATHEMATICA

b[0] = b[1] = 0; b[n_] := With[{fi = Select[FactorInteger[n], Mod[#[[1]], 4] == 1&][[All, 2]]}, (Times @@ (2*fi + 1) - 1)/2];

Table[b[n], {n, 0, 100}] // Accumulate (* Jean-Fran├žois Alcover, Feb 27 2019 *)

PROG

(PARI) a(n)=sum(a=1, n-3, sum(b=a+1, sqrtint((n-1)^2-a^2), issquare(a^2+b^2))) \\ Charles R Greathouse IV, Apr 29 2013

CROSSREFS

Cf. A156685.  Essentially partial sums of A046080.

Sequence in context: A294622 A078451 A071824 * A225370 A114540 A183142

Adjacent sequences:  A224918 A224919 A224920 * A224922 A224923 A224924

KEYWORD

nonn

AUTHOR

Reiner Moewald, Apr 19 2013

STATUS

approved

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Last modified July 24 04:08 EDT 2019. Contains 325290 sequences. (Running on oeis4.)