|
%I #7 Mar 27 2024 08:59:05
%S 1,2,6,3,12,4,10,5,15,20,16,14,7,21,24,18,22,8,28,26,13,39,27,30,34,
%T 17,51,45,9,48,32,38,19,57,63,33,11,44,40,25,75,35,56,36,52,42,46,23,
%U 69,54,50,58,29,87,90,55,80,60,76,62,31,93,96,64,82,41,123,99,66,68,85,105,49,112
%N a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number such that a(n) shares a factor with a(n-1) but sopfr(a(n)) does not share a factor with soprf(a(n-1)), where sopfr(k) is the sum of the primes dividing k, with repetition.
%C The fixed points begin 1, 2, 64, 114, 116, 132, and it is plausible no more exist. The sequence is conjectured to be a permutation of the positive integers.
%H Scott R. Shannon, <a href="/A370501/b370501.txt">Table of n, a(n) for n = 1..10000</a>
%e a(6) = 4 as a(5) = 12 and 4 shares a factor with 12 while sopfr(4) = 4 does not share a factor with sopfr(12) = 7.
%Y Cf. A001414, A370500, A370047, A370496, A352588.
%K nonn
%O 1,2
%A _Scott R. Shannon_, Feb 20 2024
|
