A220423 Cubefree products of primorials (A002110).

1, 2, 4, 6, 12, 30, 36, 60, 180, 210, 420, 900, 1260, 2310, 4620, 6300, 13860, 30030, 44100, 60060, 69300, 180180, 485100, 510510, 900900, 1021020, 3063060, 5336100, 6306300, 9699690, 15315300, 19399380, 58198140, 69369300, 107207100, 223092870, 290990700

Offset: 1

Author

Reinhard Zumkeller, Dec 14 2012

Keywords

• nonn

Comments

Suggested by a comment of Charles R Greathouse IV in A220264.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A004709 and A073491.

Cf. A000040, A001221, A001222, A002110, A006530, A051903, A064648, A212793, A220264 (subsequence).

Programs

Haskell

import Data.Set (deleteFindMin, empty, fromList, union)
import qualified Data.Set as Set (null)
a220423 n = a220423_list !! (n-1)
a220423_list = f (splitAt 1 a002110_list) empty where
   f (us'@(u:_), vs'@(v:vs)) s
     | Set.null s || m > u
                 = f (v:us', vs) (s `union` (fromList $ map (* u) us'))
     | otherwise = m : f (us', vs') s'
     where (m,s') = deleteFindMin s

Formula

A212793(a(n)) = 1; A051903(a(n)) < 3.

A001221(a(n)) <= A001222(a(n)) <= 2*A001221(a(n)).

A006530(a(n)) = A000040(A001221(a(n))).

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