|
%I #10 Apr 09 2020 05:23:48
%S 0,1,2,1,2,2,3,1,2,2,3,2,3,3,2,1,2,2,3,2,3,3,4,2,2,3,2,3,4,2,3,1,3,2,
%T 3,2,3,3,3,2,3,3,4,3,2,4,5,2,3,2,2,3,4,2,3,3,3,4,5,2,3,3,3,1,3,3,4,2,
%U 4,3,4,2,3,3,2,3,3,3,4,2,2,3,4,3,2,4,4
%N The number of iterations of the absolute Möbius divisor function (A173557) required to reach from n to 1.
%C Apparently, the least number that reaches 1 after k iterations is A082449(k-1) (checked numerically for 1 <= k <= 17).
%H Amiram Eldar, <a href="/A333870/b333870.txt">Table of n, a(n) for n = 1..10000</a>
%H Daeyeoul Kim, Umit Sarp, and Sebahattin Ikikardes, <a href="https://doi.org/10.3390/math7111083">Iterating the Sum of Möbius Divisor Function and Euler Totient Function</a>, Mathematics, Vol. 7, No. 11 (2019), pp. 1083-1094.
%e a(3) = 2 since there are 2 iterations from 3 to 1: A173557(3) = 2 and A173557(2) = 1.
%t f[p_, e_] := p - 1; u[1] = 1; u[n_] := Times @@ (f @@@ FactorInteger[n]);a[n_] := Length @ FixedPointList[u, n] - 2; Array[a, 100]
%Y Cf. A003434, A082449, A173557.
%K nonn
%O 1,3
%A _Amiram Eldar_, Apr 08 2020
|
