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A131685
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a(n) = smallest positive number m such that the sequence c(n) = { m (i^1 + 1) (i^2 + 2) ... (i^n + n) / n! : i >= 0 } takes integral values.
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,14
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COMMENTS
| It appears that none of the terms are divisible by 3 - Alexander R. Povolotsky (pevnev(AT)juno.com), Oct 18 2007
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LINKS
| Cyril Banderier, Table of n, a(n) for n = 1..100
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MAPLE
| Maple program from Cyril Banderier (Cyril.Banderier(AT)lipn.univ-paris13.fr), 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];
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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 A109939 A022619 * A019860 A011422 A051726
Adjacent sequences: A131682 A131683 A131684 * A131686 A131687 A131688
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KEYWORD
| nonn
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AUTHOR
| Alexander R. Povolotsky (pevnev(AT)juno.com) and Peter J. C. Moses (mows(AT)mopar.freeserve.co.uk), Sep 12 200, revised Sep 17 2007
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EXTENSIONS
| More terms from Cyril Banderier (Cyril.Banderier(AT)lipn.univ-paris13.fr), Sep 17 2007
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