id:A072941 - OEIS Search Results

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Least multiple of n having no prime gaps.

+0
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; listen)

	OFFSET	`1,2`
	COMMENT	`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 this_sequence A024658 A004849 A072482` `Adjacent sequences: A072938 A072939 A072940 this_sequence A072942 A072943 A072944`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 12 2002`
	EXTENSIONS	`Example corrected by Nadia Heninger (nadiah(AT)cs.princeton.edu), Jul 06 2005`

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.

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