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

Author

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

Keywords

• nonn

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

Crossrefs

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

See also A049614.

Programs

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
				

Extensions

More terms from Cyril Banderier, Sep 17 2007