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

1,2

Comments

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

Links

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

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>=1} 1/A002110(n))^k (S(1) = 1 + A064648). - Amiram Eldar, Sep 24 2023

Prog

(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

Crossrefs

Subsequence of A004709 and A073491.

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

Sequence in context: A095912 A143474 A261341 * A335068 A333931 A353899

Adjacent sequences: A220420 A220421 A220422 * A220424 A220425 A220426

Keyword

nonn

Author

Reinhard Zumkeller, Dec 14 2012

Status

approved