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%I #15 Jul 13 2013 12:02:48
%S 1,1,1,1,1,1,3,1,1,15,1,1,1,5,105,1,1155,1,1,1,35,15015,1,1,255255,
%T 385,1,5,1,4849845,1,5005,1,7,85085,111546435,1,1,3234846615,77,35,1,
%U 1616615,3,1,1,100280245065,1,385,1,3710369067405,1,1001
%N For the n-th squarefree number: the product of all primes greater than its smallest factor and less than its largest factor and not dividing it.
%C a(n)=1 iff A073484(n)=0; a(A000040(n))=1, a(A006094(n))=1, a(A002110(n))=1.
%H Reinhard Zumkeller, <a href="/A073483/b073483.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A002110(A073482(n))/(A005117(n)*A002110(A073481(n))).
%e The 69th squarefree number is 110=2*5*11, primes between 2 and 11, not dividing 110, are 3 and 7, therefore a(69)=21.
%t ppg[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]},Times@@Select[Prime[ Range[PrimePi[First[f]]+1,PrimePi[Last[f]]-1]],!MemberQ[f,#]&]]; ppg/@ Select[ Range[100],SquareFreeQ] (* _Harvey P. Dale_, Jan 16 2013 *)
%o (Haskell)
%o a073483 n = product $ filter ((> 0) . (mod m)) $
%o dropWhile (<= a020639 m) $ takeWhile (<= a006530 m) a000040_list
%o where m = a005117 n
%o -- _Reinhard Zumkeller_, Jan 15 2012
%Y Cf. A005117, A000040, A073484, A117214.
%K nonn,nice
%O 1,7
%A _Reinhard Zumkeller_, Aug 03 2002
%E a(44) and a(49) corrected by _Reinhard Zumkeller_, Jan 14 2012
%E Definition clarified by _Harvey P. Dale_, Jan 16 2013
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