A358176 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with sigma(a(n-1)).

1, 2, 3, 4, 7, 6, 8, 5, 9, 13, 10, 12, 14, 15, 16, 31, 18, 21, 20, 22, 24, 25, 62, 26, 27, 28, 30, 32, 33, 34, 36, 35, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 49, 19, 54, 55, 56, 57, 58, 60, 63, 64, 127, 66, 68, 69, 70, 72, 65, 74, 75, 76, 77, 78, 80, 81, 11, 82, 84, 86, 87, 85, 88, 90, 91, 92

Offset

1,2

Comments

The sequence is conjectured to be a permutation of the positive integers. In the first 500000 terms the fixed points are 1, 2, 3, 4, 6, 9, 12. It is unlikely more exist although this is unknown.

Links

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

Scott R. Shannon, Image of the first 200000 terms. The green line is a(n) = n.

Michael De Vlieger, Annotated log-log scatterplot of a(n), n = 1..2^14, showing records in red and local minima in blue, highlighting primes in green and other prime powers in gold. Extreme records and local minima are labeled in red and blue respectively, and composite prime powers in orange.

Example

a(8) = 5 as a(7) = 8 and sigma(8) = A000203(8) = 15, and 5 is the smallest unused number that shares a factor with 15.

Mathematica

nn = 120; c[_] = False; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; u = 3; Do[Set[{k, s}, {u, DivisorSigma[1, a[n - 1]]}]; While[Or[c[k], CoprimeQ[s, k]], k++]; Set[{a[n], c[k]}, {k, True}]; If[k == u, While[c[u], u++]], {n, 3, nn}]; Array[a, nn] (* Michael De Vlieger, Nov 05 2022 *)

Crossrefs

Cf. A000203, A358082, A358201, A064413, A356851, A356430, A354960.

Sequence in context: A130685 A210202 A358201 * A359682 A260436 A255553

Adjacent sequences: A358173 A358174 A358175 * A358177 A358178 A358179

Keyword

nonn

Author

Scott R. Shannon, Nov 02 2022

Status

approved