A143265 a(n) = the smallest integer >= n such that all the distinct primes that divide n and a(n) together are members of a set of consecutive primes. In other words, a(n) is the smallest integer >= n such that n*a(n) is contained in sequence A073491.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 11, 12, 13, 15, 15, 16, 17, 18, 19, 21, 25, 105, 23, 24, 25, 1155, 27, 30, 29, 30, 31, 32, 35, 15015, 35, 36, 37, 255255, 385, 42, 41, 45, 43, 105, 45, 4849845, 47, 48, 49, 51, 5005, 1155, 53, 54, 56, 60, 85085, 111546435, 59, 60, 61

Offset: 1

Author

Leroy Quet, Aug 03 2008

Keywords

• nonn

Examples

			20 is factored as 2^2 *5^1. Checking the integers >= 20: 20*20 is not factorable into consecutive primes, since 3 is missing. 21 is factored as 3^1 *7^1. Since the distinct primes that divide 20 and 21 (which are 2,3,5,7) form a set of consecutive primes, then a(20) = 21.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..4096 (computed from A137795 b-file)

Crossrefs

Cf. A073491, A137795.

Formula

a(n) = A137795(n) * Ceiling(n/A137795(n)). - Ray Chandler, Nov 09 2008

Extensions

Inserted a(15) and a(21) and extended by R. J. Mathar, Aug 14 2008

a(46)-a(61) from Ray Chandler, Nov 09 2008