cp's OEIS Frontend

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

%I A212617 #19 Sep 21 2013 07:30:26
%S A212617 5,10045,20475,836640,12397000,1331330000,143820000,213051960000,
%T A212617 94724270640000,3908675145375000,104284286367187500,
%U A212617 43867845932728125000000,12399293137277921875000
%N A212617 Least pentagonal number that is the product of n pentagonal numbers greater than 1.
%C A212617 10^21 < a(12) <= pen(171012369792) = 43867845932728125000000 = pen(2)^9 * pen(32) * pen(132) * pen(19439). - _Donovan Johnson_, Jun 14 2012
%H A212617 Lars Blomberg, <a href="/A212617/a212617.txt">Table of n, a(n) with solutions for n=1..13</a>
%e A212617 Let pen(n) = n*(3*n-1)/2. Then
%e A212617 a(1) = pen(2) = 5.
%e A212617 a(2) = pen(82) = 10045 = 35 * 287 = pen(5) * pen(14).
%e A212617 a(3) = pen(117) = 20475 = 5 * 35 * 117 = pen(2) * pen(5) * pen(9).
%e A212617 a(4) = pen(747) = 836640 = 5 * 12 * 12 * 1162
%e A212617      = pen(2) * pen(3)^2 * pen(28).
%e A212617 a(5) = pen(2875) = 12397000 = pen(2) * pen(4) * pen(5)^2 * pen(8).
%e A212617 a(6) = pen(29792) = 1331330000 = pen(2)^2 * pen(5)^2 * pen(11) * pen(13).
%e A212617 a(7) = pen(9792) = 143820000 = pen(2)^4 * pen(3) * pen(6) * pen(16).
%e A212617 a(8) = pen(376875) = 213051960000
%e A212617      = pen(2)^4 * pen(3)^2 * pen(4) * pen(268).
%e A212617 a(9) = pen(7946667) = 94724270640000
%e A212617      = pen(2)^3 * pen(3)^3 * pen(6) * pen(10) * pen(199).
%e A212617 a(10)= pen(51046875) = 3908675145375000
%e A212617      = pen(2)^5 * pen(4) * pen(6) * pen(8) * pen(26) * pen(90).
%e A212617 a(11)= pen(263671875) = 104284286367187500
%e A212617      = pen(2)^7 * pen(7)^2 * pen(30) * pen(369). - _Donovan Johnson_, Jun 14 2012
%Y A212617 Cf. A000326 (pentagonal numbers).
%Y A212617 Cf. A212616, A225066-A225070 (5- to 10-gonal cases).
%K A212617 nonn,more
%O A212617 1,1
%A A212617 _T. D. Noe_, Jun 12 2012
%E A212617 a(11) from _Donovan Johnson_, Jun 14 2012
%E A212617 a(12)-a(13) from _Lars Blomberg_, Sep 21 2013