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

3, 36, 300, 1485, 3240, 265356, 265356, 21520080, 21520080, 193720086, 1743362676, 141214502520, 141214502520, 11438393835996, 11438393835996, 926510072902560, 926510072902560, 75047317454789316, 75047317454789316, 6078832727785072200, 6078832727785072200

Offset: 1

Author

T. D. Noe, Jun 11 2012

Keywords

• nonn

Examples

			Contribution from _Donovan Johnson_, Jun 11 2012: (Start)
Let tri(n) = n*(n+1)/2. Then
a(1)  = 3 = tri(2).
a(2)  = 36 = tri(3)^2.
a(3)  = 300 = tri(2) * tri(4)^2.
a(4)  = 1485 = tri(2)^3 * tri(10).
a(5)  = 3240 = tri(2)^2 * tri(3)^2 * tri(4).
a(6)  = 265356 = tri(2)^4 * tri(8) * tri(13).
        265356 = tri(2)^3 * tri(3) * tri(6) * tri(12).
a(7)  = 265356 = tri(2)^4 * tri(3)^2 * tri(13).
a(8)  = 21520080 = tri(2)^6 * tri(8) * tri(40).
a(9)  = 21520080 = tri(2)^6 * tri(3)^2 * tri(40).
a(10) = 193720086 = tri(2)^7 * tri(3) * tri(6) * tri(37).
a(11) = 1743362676 = tri(2)^8  * tri(3)^2 * tri(121).
a(12) = 141214502520 = tri(2)^10 * tri(8) * tri(364).
        141214502520 = tri(2)^8 * tri(3) * tri(5) * tri(13) * tri(72).
a(13) = 141214502520 = tri(2)^10 * tri(3)^2 * tri(364).
        141214502520 = tri(2)^10 * tri(4) * tri(13) * tri(72).
a(14) = 11438393835996 = tri(2)^12 * tri(8) * tri(1093).
a(15) = 11438393835996 = tri(2)^12 * tri(3)^2 * tri(1093).
a(16) = 926510072902560 = tri(2)^14 * tri(8) * tri(3280).
a(17) = 926510072902560 = tri(2)^14 * tri(3)^2 * tri(3280).
a(18) = 75047317454789316 = tri(2)^16 * tri(8) * tri(9841).
a(19) = 75047317454789316 = tri(2)^16 * tri(3)^2 * tri(9841).
a(20) = 6078832727785072200 = tri(2)^18 * tri(8) * tri(29524).
a(21) = 6078832727785072200 = tri(2)^18 * tri(3)^2 * tri(29524). (End)
		

Crossrefs

Cf. A000217 (triangular numbers).

Cf. A212617, A225066-A225070 (5- to 10-gonal cases).

Extensions

Terms a(3) to a(21) by Donovan Johnson, Jun 11 2012