A074044 -id:A074044 - cp's OEIS frontend

A072941 Least multiple of n having no prime gaps.

1, 2, 3, 4, 5, 6, 7, 8, 9, 30, 11, 12, 13, 210, 15, 16, 17, 18, 19, 60, 105, 2310, 23, 24, 25, 30030, 27, 420, 29, 30, 31, 32, 1155, 510510, 35, 36, 37, 9699690, 15015, 120, 41, 210, 43, 4620, 45, 223092870, 47, 48, 49, 150, 255255, 60060, 53, 54, 385

Offset: 1

Reinhard Zumkeller, Aug 12 2002

a(n) = smallest m such that m is a multiple of n and in the prime factorization of m every prime between the smallest prime factor of n and the largest appears at least once.

A073490(a(n))=0; a(n)=n iff A073490(A007947(n))=0; A006530(a(n)) = A006530(n); A020639(a(n)) = A020639(n); A001221(n) <= A001221(a(n)); A001221(a(n))=A049084(A006530(n))-A049084(A020639(n))+1; A001222(n) <= A001222(a(n)); A001222(a(n)) + A001221(n) = A001221(a(n)) + A001222(n).

			a(99)=a(3*3*11)=3*3*5*7*11=3465.

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

Cf. A073490, A074044, A067255.

a072941 n = product $ zipWith (^) ps $ map (max 1) es where
            (ps, es) = unzip $ dropWhile ((== 0) . snd) $
                       zip a000040_list $ a067255_row n
-- Reinhard Zumkeller, Dec 21 2013

a(n)=A002110(A049084(A006530(n)))*A003557(n)/A002110(A049084(A020639(n))-1).

Example corrected by Nadia Heninger, Jul 06 2005

cp's OEIS Frontend

A072941 Least multiple of n having no prime gaps.

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