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a(n) = smallest positive multiple of (number of terms of {a(1), a(2), ..., a(n-1)} that are coprime to n) that is not among previous terms of sequence.
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%I #12 Dec 08 2015 08:56:43

%S 1,2,4,3,8,5,6,9,10,12,20,14,24,16,18,28,32,22,36,15,30,25,44,21,54,7,

%T 45,35,56,26,60,40,17,50,72,42,108,11,63,48,80,55,84,96,75,90,46,64,

%U 39,27,100,112,52,88,34,13,128,126,58,65,120,19,150,140,160,81,66,180,37

%N a(n) = smallest positive multiple of (number of terms of {a(1), a(2), ..., a(n-1)} that are coprime to n) that is not among previous terms of sequence.

%C This sequence does not include all positive integers; the first few omitted values are 73, 163, 177, 197, 229. At n = 931, the number of noncomposite values in the sequence exceeds 77 and numbers in this range can be divisible by at most 4 distinct primes, so any value from that point on must exceed 73. (This is not quite a proof; there could stop being any prime values in the sequence until p_k primorial catches up with the difference, but it is obvious that this does not happen.) - _Franklin T. Adams-Watters_, Jun 02 2006

%e a(8) is 9 because there are 3 terms of the sequence among the first 7 terms which are coprime to 8 and 9 is the smallest positive multiple of 3 not among the first 7 terms of the sequence.

%K nonn

%O 1,2

%A _Leroy Quet_, Sep 28 2004

%E More terms from _Franklin T. Adams-Watters_, Jun 02 2006