A225068 - OEIS

%I #6 Sep 21 2013 07:30:13

%S 8,1408,2165800,37333296,19384601600,69370076160,69370076160,

%T 56288711711232000,7917914554368000000,199449790781142859776

%N Least octagonal (8-gonal) number that is the product of n octagonal numbers greater than 1.

%H Lars Blomberg, <a href="/A225068/a225068.txt">Table of n, a(n) with solutions for n=1..10</a>

%e Let oct(n) = n*(3n-2). Then

%e a(1) = 8 = oct(2).

%e a(2) = 1408 = oct(22) = oct(2) * oct(8).

%e a(3) = 2165800 = oct(850) = oct(4) * oct(5) * oct(17).

%e a(4) = 37333296 = oct(3528) = oct(3)^2 * oct(8) * oct(13).

%e a(5) = 19384601600 = oct(80384) = oct(2)^2 * oct(5) * oct(14) * oct(53).

%e a(6) = 69370076160 = oct(152064) = oct(3)^3 * oct(4) * oct(7) * oct(22).

%Y Cf. A000567 (octagonal numbers).

%Y Cf. A212616, A212617, A225066-A225070 (3-, 5- to 10-gonal cases).

%K nonn,more

%O 1,1

%A _T. D. Noe_, May 01 2013

%E Corrected a(4) and added a(7)-a(10) by _Lars Blomberg_, Sep 21 2013