cp's OEIS Frontend

A212616 Least triangular number that is the product of n triangular numbers greater than 1.

%I A212616 #14 May 01 2013 20:53:32
%S A212616 3,36,300,1485,3240,265356,265356,21520080,21520080,193720086,
%T A212616 1743362676,141214502520,141214502520,11438393835996,11438393835996,
%U A212616 926510072902560,926510072902560,75047317454789316,75047317454789316,6078832727785072200,6078832727785072200
%N A212616 Least triangular number that is the product of n triangular numbers greater than 1.
%e A212616 Contribution from _Donovan Johnson_, Jun 11 2012: (Start)
%e A212616 Let tri(n) = n*(n+1)/2. Then
%e A212616 a(1)  = 3 = tri(2).
%e A212616 a(2)  = 36 = tri(3)^2.
%e A212616 a(3)  = 300 = tri(2) * tri(4)^2.
%e A212616 a(4)  = 1485 = tri(2)^3 * tri(10).
%e A212616 a(5)  = 3240 = tri(2)^2 * tri(3)^2 * tri(4).
%e A212616 a(6)  = 265356 = tri(2)^4 * tri(8) * tri(13).
%e A212616         265356 = tri(2)^3 * tri(3) * tri(6) * tri(12).
%e A212616 a(7)  = 265356 = tri(2)^4 * tri(3)^2 * tri(13).
%e A212616 a(8)  = 21520080 = tri(2)^6 * tri(8) * tri(40).
%e A212616 a(9)  = 21520080 = tri(2)^6 * tri(3)^2 * tri(40).
%e A212616 a(10) = 193720086 = tri(2)^7 * tri(3) * tri(6) * tri(37).
%e A212616 a(11) = 1743362676 = tri(2)^8  * tri(3)^2 * tri(121).
%e A212616 a(12) = 141214502520 = tri(2)^10 * tri(8) * tri(364).
%e A212616         141214502520 = tri(2)^8 * tri(3) * tri(5) * tri(13) * tri(72).
%e A212616 a(13) = 141214502520 = tri(2)^10 * tri(3)^2 * tri(364).
%e A212616         141214502520 = tri(2)^10 * tri(4) * tri(13) * tri(72).
%e A212616 a(14) = 11438393835996 = tri(2)^12 * tri(8) * tri(1093).
%e A212616 a(15) = 11438393835996 = tri(2)^12 * tri(3)^2 * tri(1093).
%e A212616 a(16) = 926510072902560 = tri(2)^14 * tri(8) * tri(3280).
%e A212616 a(17) = 926510072902560 = tri(2)^14 * tri(3)^2 * tri(3280).
%e A212616 a(18) = 75047317454789316 = tri(2)^16 * tri(8) * tri(9841).
%e A212616 a(19) = 75047317454789316 = tri(2)^16 * tri(3)^2 * tri(9841).
%e A212616 a(20) = 6078832727785072200 = tri(2)^18 * tri(8) * tri(29524).
%e A212616 a(21) = 6078832727785072200 = tri(2)^18 * tri(3)^2 * tri(29524). (End)
%Y A212616 Cf. A000217 (triangular numbers).
%Y A212616 Cf. A212617, A225066-A225070 (5- to 10-gonal cases).
%K A212616 nonn
%O A212616 1,1
%A A212616 _T. D. Noe_, Jun 11 2012
%E A212616 Terms a(3) to a(21) by _Donovan Johnson_, Jun 11 2012