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.

630, 990, 4095, 15400, 19110, 25200, 37128, 61425, 79800, 105570, 122265, 145530, 176715, 192510, 437580, 500500, 749700, 828828, 1185030, 2031120, 2162160, 2821500, 4279275, 4573800, 4744740, 4959675, 5364450, 6053460, 7556328, 8817900, 13857480, 15992340

Offset: 1

Author

Alex Ratushnyak, Nov 27 2017

Keywords

• nonn

Comments

Duplicates in the products are allowed.

A subsequence of A188630.

Examples

			630 = 105*6 = 21*10*3.
990 = 66*15 = 55*6*3.
		

Crossrefs

Cf. A000217, A188630.

Programs

Maple

A295769 := proc(limit) local t,E,G,n,k,j,c,b,d,ist; E:=NULL; G:=NULL;
t := proc(n) option remember; iquo(n*(n+1), 2) end;
ist := proc(n) option remember; n = t(floor(sqrt(2*n))) end;
for n from 2 do
    c := t(n); if c > limit then break fi;
    for k from 2 do
        b := c*t(k); if b > limit then break fi;
        if ist(b) then E := E, b fi;
        for j from 2 do
            d := b*t(j); if d > limit then break fi;
            if ist(d) then G := G, d fi
od od od; {E} intersect {G} end:
A295769(200000); # Peter Luschny, Dec 21 2017