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

1,3

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

Links

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A117213.

Cf. A006530, A005117, A073482, A073483.

Cf.A000720, A002110, A006530,

Sequence in context: A027642 A249306 A347427 * A185972 A182918 A134301

Adjacent sequences: A117211 A117212 A117213 * A117215 A117216 A117217

Keyword

nonn

Author

Leroy Quet, Mar 03 2006

Extensions

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

Status

approved