A117214 a(n) = (A117213(n))/(n-th squarefree positive integer).

1, 1, 2, 6, 1, 30, 3, 210, 2310, 15, 2, 30030, 510510, 10, 105, 9699690, 1155, 223092870, 1, 6469693230, 70, 15015, 6, 200560490130, 255255, 770, 7420738134810, 5, 304250263527210, 4849845, 13082761331670030, 10010

Offset: 1

Author

Leroy Quet, Mar 03 2006

Keywords

• nonn

Comments

Product of all primes up to greatest prime factor of n-th squarefree number that do not divide the n-th squarefree number. - Franklin T. Adams-Watters, Oct 09 2006

a(n) = least k such that k*A005117(n) is a primorial number. Every term is squarefree. Let m be any squarefree number, and let P be the smallest primorial such that m|P. Then a(P/m) = m, and for any primorial number Q > P, a(Q/m) = m. Since there are infinitely many Q > P it follows that every squarefree number appears in this sequence infinitely many times. - David James Sycamore, Jul 04 2024

Examples

			10 is the 7th squarefree integer. And 2*3*5 = 30 is the smallest primorial number divisible by 10 = 2*5. So a(7) = 30/10 = 3.
		

Links

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

Crossrefs

Cf. A117213.

Cf. A006530, A005117, A073482, A073483.

Cf.A000720, A002110, A006530,

Programs

Haskell

a117214 n = product $
   filter ((> 0) . (mod m)) $ takeWhile (< a006530 m) a000040_list
   where m = a005117 n
-- Reinhard Zumkeller, Jan 14 2012

Mathematica

Product[Prime@ i, {i, PrimePi@ FactorInteger[#][[-1, 1]]}]/# & /@ Select[Range@ 52, SquareFreeQ] (* Michael De Vlieger, Sep 30 2017 *)

Formula

a(n) = A002110(A000720(A005117(n))))/A005117(n). a(A002110(n)) = 1 for all n >= 0. a(A000040(n) = A002110(n-1), n > 1. - David James Sycamore, Jul 04 2024

Extensions

More terms from Franklin T. Adams-Watters, Oct 09 2006