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%I #9 Dec 22 2017 10:06:03
%S 630,990,4095,15400,19110,25200,37128,61425,79800,105570,122265,
%T 145530,176715,192510,437580,500500,749700,828828,1185030,2031120,
%U 2162160,2821500,4279275,4573800,4744740,4959675,5364450,6053460,7556328,8817900,13857480,15992340
%N Triangular numbers that can be represented as a product of two triangular numbers greater than 1, and as a product of three triangular numbers greater than 1.
%C Duplicates in the products are allowed.
%C A subsequence of A188630.
%e 630 = 105*6 = 21*10*3.
%e 990 = 66*15 = 55*6*3.
%p A295769 := proc(limit) local t,E,G,n,k,j,c,b,d,ist; E:=NULL; G:=NULL;
%p t := proc(n) option remember; iquo(n*(n+1), 2) end;
%p ist := proc(n) option remember; n = t(floor(sqrt(2*n))) end;
%p for n from 2 do
%p c := t(n); if c > limit then break fi;
%p for k from 2 do
%p b := c*t(k); if b > limit then break fi;
%p if ist(b) then E := E, b fi;
%p for j from 2 do
%p d := b*t(j); if d > limit then break fi;
%p if ist(d) then G := G, d fi
%p od od od; {E} intersect {G} end:
%p A295769(200000); # _Peter Luschny_, Dec 21 2017
%Y Cf. A000217, A188630.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, Nov 27 2017
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