cp's OEIS Frontend

A224921 Number of Pythagorean triples (a, b, c) with a^2 + b^2 = c^2 and 0 < a < b < c < n.

%I A224921 #41 Dec 11 2021 04:31:51
%S A224921 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,
%T A224921 11,11,12,13,13,14,14,15,16,17,17,17,17,18,18,18,18,18,20,21,22,23,23,
%U A224921 24,24,24,25,25,26,27,27,27,27,31,31,31,32,32,33,33,33
%N A224921 Number of Pythagorean triples (a, b, c) with a^2 + b^2 = c^2 and 0 < a < b < c < n.
%C A224921 a(n+1) > a(n) iff n is in A009003. - _Benoit Cloitre_, Dec 08 2021
%H A224921 Reiner Moewald and Robert Israel, <a href="/A224921/b224921.txt">Table of n, a(n) for n = 1..10000</a> (n = 1..500 from Reiner Moewald)
%p A224921 a046080:= proc(n) local F,t;
%p A224921   F:= select(t -> t[1] mod 4 = 1, ifactors(n)[2]);
%p A224921   1/2*(mul(2*t[2]+1, t=F)-1)
%p A224921 end proc:
%p A224921 ListTools:-PartialSums(map(a046080, [$0..100])); # _Robert Israel_, Jul 18 2016
%t A224921 b[0] = b[1] = 0; b[n_] := With[{fi = Select[FactorInteger[n], Mod[#[[1]], 4] == 1&][[All, 2]]}, (Times @@ (2*fi + 1) - 1)/2];
%t A224921 Table[b[n], {n, 0, 100}] // Accumulate (* _Jean-François Alcover_, Feb 27 2019 *)
%o A224921 (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
%Y A224921 Cf. A156685. Essentially partial sums of A046080.
%Y A224921 Cf. A009003.
%K A224921 nonn
%O A224921 1,11
%A A224921 _Reiner Moewald_, Apr 19 2013