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.

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

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

Cf. A005117, A000040, A073484, A117214.

Sequence in context: A156869 A153090 A203002 * A006956 A072285 A144269

Adjacent sequences: A073480 A073481 A073482 * A073484 A073485 A073486

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