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

Author

Jud McCranie, May 31 2000

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A000203, A055021.

Programs

Mathematica

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

PARI

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