A348337 For n >= 1; x = n, then iterate x --> x + d(x) until d(x + d(x)) >= d(x). a(n) gives the number of iteration steps where d(i) is the number of divisors of i, A000005(i).

3, 2, 7, 1, 6, 5, 5, 4, 4, 4, 3, 3, 2, 3, 1, 1, 3, 2, 2, 1, 1, 3, 3, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 2, 2, 1, 2, 3, 1, 2, 3, 1, 3, 3, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 3, 3, 6, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 3, 5, 2, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 4, 1, 2, 5, 4, 5, 1, 4, 4, 1, 4, 3, 3, 3, 3, 2, 1

Offset

1,1

Comments

a(n) = 1 for n from A260577.

Links

Table of n, a(n) for n=1..100.

Example

n = 1; x(1) = 1 + d(1) = 2, d(1 + d(1)) >= d(1) thus x(2) = 2 + d(2) = 4, d(2 + d(2)) >= d(2) thus x(3) = 4 + d(4) = 7, d(4 + d(4)) < d(4), stop. a(1) = 3.

Mathematica

d[n_] := DivisorSigma[0, n]; x[n_] := n + d[n]; a[n_] := Length@ NestWhileList[x, n, d[#] <= d[x[#]] &]; Array[a, 100] (* Amiram Eldar, Oct 15 2021 *)

Crossrefs

Cf. A000005, A062249, A175304, A259934, A260577, A286529.

Sequence in context: A373485 A369045 A163659 * A010760 A085594 A085587

Adjacent sequences: A348334 A348335 A348336 * A348338 A348339 A348340

Keyword

nonn

Author

Ctibor O. Zizka, Oct 13 2021

Status

approved