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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A063379 A000463 A137442 * A129596 A284572 A157182

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

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Last modified June 18 17:05 EDT 2019. Contains 324214 sequences. (Running on oeis4.)