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

1,1

Links

Table of n, a(n) for n=1..21.

Example

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).

Sequence in context: A005446 A056307 A056299 * A073980 A034860 A220831

Adjacent sequences: A212613 A212614 A212615 * A212617 A212618 A212619

Keyword

nonn

Author

T. D. Noe, Jun 11 2012

Extensions

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

Status

approved