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

%I A117214 #30 Jul 07 2024 20:58:53
%S A117214 1,1,2,6,1,30,3,210,2310,15,2,30030,510510,10,105,9699690,1155,
%T A117214 223092870,1,6469693230,70,15015,6,200560490130,255255,770,
%U A117214 7420738134810,5,304250263527210,4849845,13082761331670030,10010
%N A117214 a(n) = (A117213(n))/(n-th squarefree positive integer).
%C A117214 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
%C A117214 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
%H A117214 Reinhard Zumkeller, <a href="/A117214/b117214.txt">Table of n, a(n) for n = 1..1000</a>
%F A117214 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
%e A117214 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.
%t A117214 Product[Prime@ i, {i, PrimePi@ FactorInteger[#][[-1, 1]]}]/# & /@ Select[Range@ 52, SquareFreeQ] (* _Michael De Vlieger_, Sep 30 2017 *)
%o A117214 (Haskell)
%o A117214 a117214 n = product $
%o A117214    filter ((> 0) . (mod m)) $ takeWhile (< a006530 m) a000040_list
%o A117214    where m = a005117 n
%o A117214 -- _Reinhard Zumkeller_, Jan 14 2012
%Y A117214 Cf. A117213.
%Y A117214 Cf. A006530, A005117, A073482, A073483.
%Y A117214 Cf.A000720, A002110, A006530,
%K A117214 nonn
%O A117214 1,3
%A A117214 _Leroy Quet_, Mar 03 2006
%E A117214 More terms from _Franklin T. Adams-Watters_, Oct 09 2006