A143265 - OEIS

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.

%I #8 Sep 27 2019 11:44:48

%S 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,

%T 1155,27,30,29,30,31,32,35,15015,35,36,37,255255,385,42,41,45,43,105,

%U 45,4849845,47,48,49,51,5005,1155,53,54,56,60,85085,111546435,59,60,61

%N 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.

%H Ray Chandler, <a href="/A143265/b143265.txt">Table of n, a(n) for n = 1..4096</a> (computed from A137795 b-file)

%F a(n) = A137795(n) * Ceiling(n/A137795(n)). - _Ray Chandler_, Nov 09 2008

%e 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.

%Y Cf. A073491, A137795.

%K nonn

%O 1,2

%A _Leroy Quet_, Aug 03 2008

%E Inserted a(15) and a(21) and extended by _R. J. Mathar_, Aug 14 2008

%E a(46)-a(61) from _Ray Chandler_, Nov 09 2008