A355374 - OEIS

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 #14 Jul 03 2022 09:11:28

%S 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 18,289,33,361,20,529,34,841,28,35,38,39,2401,32,13,46,14641,24,961,

%U 44,51,28561,48,1369,64,17,1681,45,83521,729,15625,30,130321,1024,19,55,50,57,279841,117649

%N 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 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 Scott R. Shannon, <a href="/A355374/b355374.txt">Table of n, a(n) for n = 1..713</a>

%e 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 Cf. A000120, A032741, A005179, A027751.

%K nonn,base,look

%O 1,2

%A _Scott R. Shannon_, Jun 30 2022