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Number of iterations of sigma() required until 2n (or greater) is reached.
5

%I #13 Mar 18 2024 03:30:08

%S 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,

%T 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,

%U 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

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

%H Amiram Eldar, <a href="/A055020/b055020.txt">Table of n, a(n) for n = 2..10001</a>

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

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

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

%Y Cf. A000203, A055021.

%K nonn

%O 2,1

%A _Jud McCranie_, May 31 2000