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).

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, 28, 32, 20, 36, 26, 35, 33, 34, 37, 43, 29, 39, 40, 46, 31, 48, 38, 47, 49, 44, 41, 56, 45, 53, 51, 55, 42, 60, 54, 62, 57, 58, 50, 70, 52, 63, 66, 68, 64, 72, 59, 71, 67, 76, 61, 82

Offset: 1

Author

Leroy Quet, Nov 29 2001

Keywords

• nonn

Comments

Every positive integer occurs once and only once somewhere in this sequence.

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A065578, A065562.

Programs

Mathematica

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 *)