|
%I #20 Feb 02 2015 21:51:24
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,7,7,7,1,1,1,1,1,11,11,11,55,143,13,91,91,
%T 91,91,91,1001,17017,595595,595595,17017,46189,600457,3002285,3002285,
%U 3002285,3002285,6605027,3002285,726869,726869,726869
%N a(n) = smallest positive number m such that c(i) = m (i^1 + 1) (i^2 + 2) ... (i^n + n) / n! takes integral values for all i>=0.
%C It appears that none of the terms are divisible by 3. - _Alexander R. Povolotsky_, Oct 18 2007
%H Cyril Banderier, <a href="/A131685/b131685.txt">Table of n, a(n) for n = 1..100</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%p # Maple program from _Cyril Banderier_, Sep 18 2007:
%p List:=NULL: for n from 1 to 1000 do m:=1: #running till n=50 will last 2 min.
%p for i from 1 to numtheory[pi](n) do div:=ithprime(i): d:=1: e:=0: oldmini:=-1:mini:=0:
%p while oldmini<>mini do e:=e+1: #the last time consuming loop could be skipped by proving e<=floor(ln(n)/ln(div)):
%p d:=d*div;for x from 0 to d-1 do [seq((x &^k mod d)+k mod d,k=1..n)]:contrib[d,x]:=nops(select(has,%,0)): od:
%p L:=seq(add(contrib[div^j,x mod div^j],j=1..e),x=0..div^e-1); oldmini:=mini: mini:=min(L): od:
%p if mini<padic[ordp](n!,div) then m:=m*div^(padic[ordp](n!,div)-mini) fi; od: print(n,m); List:=List,m: od:
%p [List];
%Y Cf. A000027 (for n=1), A064808 (n=2), A131509 (n=3), A129995 (n=4), A131675 (n=5), ..., A131680 (n=10).
%Y See also A049614.
%K nonn
%O 1,14
%A _Alexander R. Povolotsky_ and _Peter J. C. Moses_, Sep 12 2007, revised Sep 17 2007
%E More terms from _Cyril Banderier_, Sep 17 2007
|
