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

1,2

Comments

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

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Example

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.

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 *)

Crossrefs

Cf. A065578, A065562.

Sequence in context: A364225 A256995 A249129 * A245708 A126917 A250471

Adjacent sequences: A065558 A065559 A065560 * A065562 A065563 A065564

Keyword

nonn

Author

Leroy Quet, Nov 29 2001

Status

approved