A111390 a(1)=1. a(n) = smallest positive integer not occurring earlier in the sequence such that |d(a(n))-d(a(n-1))| = 1, where d(n) is the number of positive divisors of n.

1, 2, 4, 3, 9, 5, 25, 6, 16, 8, 49, 7, 121, 10, 81, 12, 64, 18, 625, 14, 169, 11, 289, 13, 361, 15, 529, 17, 841, 19, 961, 21, 1369, 22, 1681, 23, 1849, 26, 2209, 27, 2401, 20, 729, 24, 36, 30, 100, 40, 196, 42, 225, 48, 256, 54, 441, 56, 484, 66, 676, 70, 1089, 78, 1156, 80

Offset

1,2

Comments

Sequence is a permutation of the positive integers.

Terms a(65) to a(76) are 1024, 60, 4096, 72, 59049, 84, 531441, 90, 9765625, 96, 244140625, 108. - Klaus Brockhaus, Nov 13 2005

Links

Table of n, a(n) for n=1..64.

Example

Among positive integers not among the first 4 terms of the sequence, a(5) = 9 is the lowest such that |d(a(5))-d(a(4))| = |d(9)-d(3)| = |3-2| is 1.

Mathematica

Block[{a = {1}, k}, Do[k = 2; While[Nand[FreeQ[a, k], Abs[DivisorSigma[0, k] - DivisorSigma[0, a[[i]]]] == 1], k++]; AppendTo[a, k], {i, 63}]; a] (* Michael De Vlieger, Sep 11 2017 *)

Crossrefs

Cf. A114107 (inverse), A114108 (number of divisors), A114109 (fixed points), A114110 (records), A114111 (where records occur).

Sequence in context: A358534 A137442 A350150 * A349323 A344554 A129596

Adjacent sequences: A111387 A111388 A111389 * A111391 A111392 A111393

Keyword

nonn

Author

Leroy Quet, Nov 10 2005

Extensions

More terms from Klaus Brockhaus, Nov 11 2005

Status

approved