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A355374 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared such that the number of proper divisors of a(n) equals the number of 1-bits in the binary expansion of a(n-1).

%I A355374 #14 Jul 03 2022 09:11:28
%S A355374 1,2,3,4,5,9,25,6,49,8,7,10,121,12,169,16,11,14,15,81,21,22,26,27,625,
%T A355374 18,289,33,361,20,529,34,841,28,35,38,39,2401,32,13,46,14641,24,961,
%U A355374 44,51,28561,48,1369,64,17,1681,45,83521,729,15625,30,130321,1024,19,55,50,57,279841,117649
%N A355374 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared such that the number of proper divisors of a(n) equals the number of 1-bits in the binary expansion of a(n-1).
%C A355374 In the first 700 terms the fixed points are 1, 2, 3, 4, 5, 16, 21, 22, 35, 48, 168, 412, 428. The sequence is conjectured to be a permutation of the positive integers.
%H A355374 Scott R. Shannon, <a href="/A355374/b355374.txt">Table of n, a(n) for n = 1..713</a>
%e A355374 a(7) = 25 as a(6) = 9 = 1001_2 which has two 1-bits in its binary expansion, and 25 is the smallest unused number that has two proper divisors.
%Y A355374 Cf. A000120, A032741, A005179, A027751.
%K A355374 nonn,base,look
%O A355374 1,2
%A A355374 _Scott R. Shannon_, Jun 30 2022