cp's OEIS Frontend

A131685 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.

%I A131685 #20 Feb 02 2015 21:51:24
%S A131685 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 A131685 91,91,91,1001,17017,595595,595595,17017,46189,600457,3002285,3002285,
%U A131685 3002285,3002285,6605027,3002285,726869,726869,726869
%N A131685 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 A131685 It appears that none of the terms are divisible by 3. - _Alexander R. Povolotsky_, Oct 18 2007
%H A131685 Cyril Banderier, <a href="/A131685/b131685.txt">Table of n, a(n) for n = 1..100</a>
%H A131685 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%p A131685 # Maple program from _Cyril Banderier_, Sep 18 2007:
%p A131685 List:=NULL: for n from 1 to 1000 do m:=1: #running till n=50 will last 2 min.
%p A131685 for i from 1 to numtheory[pi](n) do div:=ithprime(i): d:=1: e:=0: oldmini:=-1:mini:=0:
%p A131685 while oldmini<>mini do e:=e+1: #the last time consuming loop could be skipped by proving e<=floor(ln(n)/ln(div)):
%p A131685 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 A131685 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 A131685 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 A131685 [List];
%Y A131685 Cf. A000027 (for n=1), A064808 (n=2), A131509 (n=3), A129995 (n=4), A131675 (n=5), ..., A131680 (n=10).
%Y A131685 See also A049614.
%K A131685 nonn
%O A131685 1,14
%A A131685 _Alexander R. Povolotsky_ and _Peter J. C. Moses_, Sep 12 2007, revised Sep 17 2007
%E A131685 More terms from _Cyril Banderier_, Sep 17 2007