A072941 - OEIS

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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 (list; graph; refs; listen; history; 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).`
	FORMULA	`a(n)=A002110(A049084(A006530(n)))*A003557(n)/A002110(A049084(A020639(n))-1).`
	EXAMPLE	`a(99)=a(3311)=335711=3465.`
	CROSSREFS	`Cf. A073490, A073490, A074044.` `Sequence in context: A031309 A122621 A118767 * A024658 A004849 A173551` `Adjacent sequences: A072938 A072939 A072940 * A072942 A072943 A072944`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 12 2002`
	EXTENSIONS	`Example corrected by Nadia Heninger (nadiah(AT)cs.princeton.edu), Jul 06 2005`

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Last modified February 17 11:46 EST 2012. Contains 206011 sequences.