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A220423 Cubefree products of primorials (A002110).

%I A220423 #19 Nov 01 2024 23:39:09
%S A220423 1,2,4,6,12,30,36,60,180,210,420,900,1260,2310,4620,6300,13860,30030,
%T A220423 44100,60060,69300,180180,485100,510510,900900,1021020,3063060,
%U A220423 5336100,6306300,9699690,15315300,19399380,58198140,69369300,107207100,223092870,290990700
%N A220423 Cubefree products of primorials (A002110).
%C A220423 Suggested by a comment of _Charles R Greathouse IV_ in A220264.
%H A220423 Reinhard Zumkeller, <a href="/A220423/b220423.txt">Table of n, a(n) for n = 1..10000</a>
%F A220423 A212793(a(n)) = 1; A051903(a(n)) < 3.
%F A220423 A001221(a(n)) <= A001222(a(n)) <= 2*A001221(a(n)).
%F A220423 A006530(a(n)) = A000040(A001221(a(n))).
%F A220423 Sum_{n>=1} 1/a(n) = (S(1)^2 + S(2))/2 = 2.093360845965235020766040..., where S(k) = Sum_{n>=0} 1/(A002110(n))^k (S(1) = 1 + A064648). - _Amiram Eldar_, Sep 24 2023
%o A220423 (Haskell)
%o A220423 import Data.Set (deleteFindMin, empty, fromList, union)
%o A220423 import qualified Data.Set as Set (null)
%o A220423 a220423 n = a220423_list !! (n-1)
%o A220423 a220423_list = f (splitAt 1 a002110_list) empty where
%o A220423    f (us'@(u:_), vs'@(v:vs)) s
%o A220423      | Set.null s || m > u
%o A220423                  = f (v:us', vs) (s `union` (fromList $ map (* u) us'))
%o A220423      | otherwise = m : f (us', vs') s'
%o A220423      where (m,s') = deleteFindMin s
%Y A220423 Subsequence of A004709 and A073491.
%Y A220423 Cf. A000040, A001221, A001222, A002110, A006530, A051903, A064648, A212793, A220264 (subsequence).
%K A220423 nonn
%O A220423 1,2
%A A220423 _Reinhard Zumkeller_, Dec 14 2012