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A212617 Least pentagonal number that is the product of n pentagonal numbers greater than 1. 7
5, 10045, 20475, 836640, 12397000, 1331330000, 143820000, 213051960000, 94724270640000, 3908675145375000, 104284286367187500, 43867845932728125000000, 12399293137277921875000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 11 21:15 EST 2017. Contains 295919 sequences.