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

1,1

Comments

Duplicates in the products are allowed.

A subsequence of A188630.

Links

Table of n, a(n) for n=1..32.

Example

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

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

Crossrefs

Cf. A000217, A188630.

Sequence in context: A177421 A333503 A173423 * A110904 A171258 A234245

Adjacent sequences: A295766 A295767 A295768 * A295770 A295771 A295772

Keyword

nonn

Author

Alex Ratushnyak, Nov 27 2017

Status

approved