%I #14 May 01 2013 20:53:32
%S 3,36,300,1485,3240,265356,265356,21520080,21520080,193720086,
%T 1743362676,141214502520,141214502520,11438393835996,11438393835996,
%U 926510072902560,926510072902560,75047317454789316,75047317454789316,6078832727785072200,6078832727785072200
%N Least triangular number that is the product of n triangular numbers greater than 1.
%e Contribution from _Donovan Johnson_, Jun 11 2012: (Start)
%e Let tri(n) = n*(n+1)/2. Then
%e a(1) = 3 = tri(2).
%e a(2) = 36 = tri(3)^2.
%e a(3) = 300 = tri(2) * tri(4)^2.
%e a(4) = 1485 = tri(2)^3 * tri(10).
%e a(5) = 3240 = tri(2)^2 * tri(3)^2 * tri(4).
%e a(6) = 265356 = tri(2)^4 * tri(8) * tri(13).
%e 265356 = tri(2)^3 * tri(3) * tri(6) * tri(12).
%e a(7) = 265356 = tri(2)^4 * tri(3)^2 * tri(13).
%e a(8) = 21520080 = tri(2)^6 * tri(8) * tri(40).
%e a(9) = 21520080 = tri(2)^6 * tri(3)^2 * tri(40).
%e a(10) = 193720086 = tri(2)^7 * tri(3) * tri(6) * tri(37).
%e a(11) = 1743362676 = tri(2)^8 * tri(3)^2 * tri(121).
%e a(12) = 141214502520 = tri(2)^10 * tri(8) * tri(364).
%e 141214502520 = tri(2)^8 * tri(3) * tri(5) * tri(13) * tri(72).
%e a(13) = 141214502520 = tri(2)^10 * tri(3)^2 * tri(364).
%e 141214502520 = tri(2)^10 * tri(4) * tri(13) * tri(72).
%e a(14) = 11438393835996 = tri(2)^12 * tri(8) * tri(1093).
%e a(15) = 11438393835996 = tri(2)^12 * tri(3)^2 * tri(1093).
%e a(16) = 926510072902560 = tri(2)^14 * tri(8) * tri(3280).
%e a(17) = 926510072902560 = tri(2)^14 * tri(3)^2 * tri(3280).
%e a(18) = 75047317454789316 = tri(2)^16 * tri(8) * tri(9841).
%e a(19) = 75047317454789316 = tri(2)^16 * tri(3)^2 * tri(9841).
%e a(20) = 6078832727785072200 = tri(2)^18 * tri(8) * tri(29524).
%e a(21) = 6078832727785072200 = tri(2)^18 * tri(3)^2 * tri(29524). (End)
%Y Cf. A000217 (triangular numbers).
%Y Cf. A212617, A225066-A225070 (5- to 10-gonal cases).
%K nonn
%O 1,1
%A _T. D. Noe_, Jun 11 2012
%E Terms a(3) to a(21) by _Donovan Johnson_, Jun 11 2012
|