A212617 Least pentagonal number that is the product of n pentagonal numbers greater than 1.

5, 10045, 20475, 836640, 12397000, 1331330000, 143820000, 213051960000, 94724270640000, 3908675145375000, 104284286367187500, 43867845932728125000000, 12399293137277921875000

Offset

1,1

Comments

10^21 < a(12) <= pen(171012369792) = 43867845932728125000000 = pen(2)^9 * pen(32) * pen(132) * pen(19439). - Donovan Johnson, Jun 14 2012

Links

Table of n, a(n) for n=1..13.

Lars Blomberg, Table of n, a(n) with solutions for n=1..13

Example

Let pen(n) = n*(3*n-1)/2. Then
a(1) = pen(2) = 5.
a(2) = pen(82) = 10045 = 35 * 287 = pen(5) * pen(14).
a(3) = pen(117) = 20475 = 5 * 35 * 117 = pen(2) * pen(5) * pen(9).
a(4) = pen(747) = 836640 = 5 * 12 * 12 * 1162
     = pen(2) * pen(3)^2 * pen(28).
a(5) = pen(2875) = 12397000 = pen(2) * pen(4) * pen(5)^2 * pen(8).
a(6) = pen(29792) = 1331330000 = pen(2)^2 * pen(5)^2 * pen(11) * pen(13).
a(7) = pen(9792) = 143820000 = pen(2)^4 * pen(3) * pen(6) * pen(16).
a(8) = pen(376875) = 213051960000
     = pen(2)^4 * pen(3)^2 * pen(4) * pen(268).
a(9) = pen(7946667) = 94724270640000
     = pen(2)^3 * pen(3)^3 * pen(6) * pen(10) * pen(199).
a(10)= pen(51046875) = 3908675145375000
     = pen(2)^5 * pen(4) * pen(6) * pen(8) * pen(26) * pen(90).
a(11)= pen(263671875) = 104284286367187500
     = pen(2)^7 * pen(7)^2 * pen(30) * pen(369). - Donovan Johnson, Jun 14 2012

Crossrefs

Cf. A000326 (pentagonal numbers).

Cf. A212616, A225066-A225070 (5- to 10-gonal cases).

Sequence in context: A052027 A109514 A022918 * A160741 A101846 A292742

Adjacent sequences: A212614 A212615 A212616 * A212618 A212619 A212620

Keyword

nonn,more

Author

T. D. Noe, Jun 12 2012

Extensions

a(11) from Donovan Johnson, Jun 14 2012

a(12)-a(13) from Lars Blomberg, Sep 21 2013

Status

approved