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

Author

Reinhard Zumkeller, Aug 03 2002

Keywords

• nonn
• nice

Comments

a(n)=1 iff A073484(n)=0; a(A000040(n))=1, a(A006094(n))=1, a(A002110(n))=1.

Examples

			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.
		

Links

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

Crossrefs

Cf. A005117, A000040, A073484, A117214.

Programs

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

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 *)

Formula

a(n) = A002110(A073482(n))/(A005117(n)*A002110(A073481(n))).

Extensions

a(44) and a(49) corrected by Reinhard Zumkeller, Jan 14 2012

Definition clarified by Harvey P. Dale, Jan 16 2013