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 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. 16
 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; text; internal format)
 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 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

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)