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.

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, 91, 91, 91, 1001, 17017, 595595, 595595, 17017, 46189, 600457, 3002285, 3002285, 3002285, 3002285, 6605027, 3002285, 726869, 726869, 726869

Offset

1,14

Comments

It appears that none of the terms are divisible by 3. - Alexander R. Povolotsky, Oct 18 2007

Links

Cyril Banderier, Table of n, a(n) for n = 1..100

Index to divisibility sequences

Maple

# Maple program from Cyril Banderier, Sep 18 2007:
List:=NULL: for n from 1 to 1000 do m:=1: #running till n=50 will last 2 min.
for i from 1 to numtheory[pi](n) do div:=ithprime(i): d:=1: e:=0: oldmini:=-1:mini:=0:
while oldmini<>mini do e:=e+1: #the last time consuming loop could be skipped by proving e<=floor(ln(n)/ln(div)):
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:
L:=seq(add(contrib[div^j, x mod div^j], j=1..e), x=0..div^e-1); oldmini:=mini: mini:=min(L): od:
if mini<padic[ordp](n!, div) then m:=m*div^(padic[ordp](n!, div)-mini) fi; od: print(n, m); List:=List, m: od:
[List];

Crossrefs

Cf. A000027 (for n=1), A064808 (n=2), A131509 (n=3), A129995 (n=4), A131675 (n=5), ..., A131680 (n=10).

See also A049614.

Sequence in context: A195202 A252799 A022619 * A019860 A011422 A051726

Adjacent sequences: A131682 A131683 A131684 * A131686 A131687 A131688

Keyword

nonn

Author

Alexander R. Povolotsky and Peter J. C. Moses, Sep 12 2007, revised Sep 17 2007

Extensions

More terms from Cyril Banderier, Sep 17 2007

Status

approved