A055020 Number of iterations of sigma() required until 2n (or greater) is reached.

2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 3, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 3, 2, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 2, 1, 4, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 3, 2, 2, 1, 2, 1, 2, 1

Offset

2,1

Links

Amiram Eldar, Table of n, a(n) for n = 2..10001

Example

sigma(sigma(sigma(9))) = 24 >= 2*9, so a(9) = 3.

Mathematica

a[n_] := -1 + Length@ NestWhileList[DivisorSigma[1, #] &, n, # < 2*n &]; Array[a, 100, 2] (* Amiram Eldar, Mar 18 2024 *)

Prog

(PARI) a(n) = {my(m = n, nn = 2*n, c = 0); while(m < nn, m = sigma(m); c++); c; } \\ Amiram Eldar, Mar 18 2024

Crossrefs

Cf. A000203, A055021.

Sequence in context: A318882 A327160 A355832 * A052435 A094701 A210452

Adjacent sequences: A055017 A055018 A055019 * A055021 A055022 A055023

Keyword

nonn

Author

Jud McCranie, May 31 2000

Status

approved