cp's OEIS Frontend

A295769 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.

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