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A072941 Least multiple of n having no prime gaps. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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).

LINKS

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

FORMULA

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

EXAMPLE

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

PROG

(Haskell)

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

CROSSREFS

Cf. A073490, A074044, A067255.

Sequence in context: A122621 A229547 A118767 * A225655 A024658 A004849

Adjacent sequences:  A072938 A072939 A072940 * A072942 A072943 A072944

KEYWORD

nonn,look

AUTHOR

Reinhard Zumkeller, Aug 12 2002

EXTENSIONS

Example corrected by Nadia Heninger, Jul 06 2005

STATUS

approved

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Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)