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A073483
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.
6
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, 385, 1, 5, 1, 4849845, 1, 5005, 1, 7, 85085, 111546435, 1, 1, 3234846615, 77, 35, 1, 1616615, 3, 1, 1, 100280245065, 1, 385, 1, 3710369067405, 1, 1001
OFFSET
1,7
COMMENTS
a(n)=1 iff A073484(n)=0; a(A000040(n))=1, a(A006094(n))=1, a(A002110(n))=1.
LINKS
FORMULA
a(n) = A002110(A073482(n))/(A005117(n)*A002110(A073481(n))).
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(Haskell)
a073483 n = product $ filter ((> 0) . (mod m)) $
dropWhile (<= a020639 m) $ takeWhile (<= a006530 m) a000040_list
where m = a005117 n
-- Reinhard Zumkeller, Jan 15 2012
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Reinhard Zumkeller, Aug 03 2002
EXTENSIONS
a(44) and a(49) corrected by Reinhard Zumkeller, Jan 14 2012
Definition clarified by Harvey P. Dale, Jan 16 2013
STATUS
approved