cp's OEIS Frontend

A370500 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number such that a(n) does not share a factor with a(n-1) but sopfr(a(n)) does share a factor with soprf(a(n-1)), where sopfr(k) is the sum of the primes dividing k, with repetition.

%I A370500 #10 Mar 27 2024 08:59:10
%S A370500 1,2,9,4,15,8,3,14,27,20,77,16,21,5,6,25,18,35,24,65,32,33,7,10,49,12,
%T A370500 115,36,55,39,50,51,26,81,38,105,44,91,30,119,57,11,28,45,62,85,42,95,
%U A370500 64,69,13,22,63,74,75,56,169,60,121,40,123,70,87,98,93,17,52,99,145,66,133,72,125,46
%N A370500 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number such that a(n) does not share a factor with a(n-1) but sopfr(a(n)) does share a factor with soprf(a(n-1)), where sopfr(k) is the sum of the primes dividing k, with repetition.
%C A370500 The fixed points begin 1, 2, 4, 56, 72, 138, 200, 438, 500, 540, 590, 3998. The sequence is conjectured to be a permutation of the positive integers.
%H A370500 Scott R. Shannon, <a href="/A370500/b370500.txt">Table of n, a(n) for n = 1..10000</a>
%e A370500 a(4) = 4 as a(3) = 9 and 4 does not share a factor with 9 while sopfr(4) = 4 does share a factor with sopfr(9) = 6.
%Y A370500 Cf. A001414, A370501, A370047, A370496, A352588.
%K A370500 nonn
%O A370500 1,2
%A A370500 _Scott R. Shannon_, Feb 20 2024