A055020 - OEIS

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

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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