A267141 - OEIS

%I #25 Jun 16 2018 15:59:10

%S 6,66,792,10296,144144,2162160,34594560,588107520,10585935360,

%T 201132771840,4022655436800,84475764172800,1858466811801600,

%U 42744736671436800,1025873680114483200,25646842002862080000,666817892074414080000

%N Number of weeks in n! seconds, for n >= 10.

%C 10! seconds = 6 weeks (exactly)

%C 11! seconds = 66 weeks (exactly)

%C 12! seconds = 792 weeks (exactly), etc.

%C Demonstration of first term:

%C   6 w * 7 d/w * 24 h/d * 60 m/h * 60 s/m  = seconds in 6 weeks =

%C   (2*3)*(1*7)  *(3*8)  * (6*10) * (3*5*4) =

%C   1*2*3*4*5*6*7*8*(3^2)*10                = 10! seconds

%H Brady Haran, James Grime, <a href="https://www.youtube.com/watch?v=kUBIJdGsD1A">10!</a>, Numberphile video (2012)

%F a(n) = 6*n!/10!.

%F a(n) = 6*A051431(n-10), for n>=10.

%e For n=12, a(12) = 6*(12)!/10! = 792; interpretation: 12! seconds = 792 weeks.

%t f[n_] := n!/(60*60*24*7); Array[f, 17, 10] (* _Robert G. Wilson v_, Jan 12 2016 *)

%o (PARI) a(n) = 6*n!/10!; \\ _Altug Alkan_, Jan 12 2016

%Y Cf. A051431.

%K easy,nonn

%O 10,1

%A _Richard H. Sweetman_, Jan 10 2016