cp's OEIS Frontend

A065561 a(1) = 1; for n >= 2, a(n) = (d(n)-1)-th highest positive integer that equals no a(k), 1 <= k < n, where d(n) is the number of positive divisors of n, A000005(n).

%I A065561 #18 Dec 12 2017 00:31:48
%S A065561 1,2,3,5,4,8,6,10,9,12,7,16,11,15,17,19,13,22,14,24,21,23,18,30,25,27,
%T A065561 28,32,20,36,26,35,33,34,37,43,29,39,40,46,31,48,38,47,49,44,41,56,45,
%U A065561 53,51,55,42,60,54,62,57,58,50,70,52,63,66,68,64,72,59,71,67,76,61,82
%N A065561 a(1) = 1; for n >= 2, a(n) = (d(n)-1)-th highest positive integer that equals no a(k), 1 <= k < n, where d(n) is the number of positive divisors of n, A000005(n).
%C A065561 Every positive integer occurs once and only once somewhere in this sequence.
%H A065561 Michael De Vlieger, <a href="/A065561/b065561.txt">Table of n, a(n) for n = 1..10000</a>
%H A065561 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A065561 d(6)-1 = 3 and the 3rd-highest positive integer not equal to 1, 2, 3, 5, or 4 (the values of a(k) for 1 <= k < 6) is 8.
%t A065561 With[{nn = 72}, Fold[Append[#1, Complement[Range[#2 + Ceiling[nn/6]], #1][[DivisorSigma[0, #2] - 1]]] &, {1}, Range[2, nn]]] (* _Michael De Vlieger_, Dec 11 2017 *)
%Y A065561 Cf. A065578, A065562.
%K A065561 nonn
%O A065561 1,2
%A A065561 _Leroy Quet_, Nov 29 2001