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Number of steps to reach 1 by iterating the alternating sum of divisors function A071324 starting from n.
3

%I #7 Mar 14 2020 04:43:23

%S 0,1,2,3,4,4,5,5,6,5,6,6,7,6,7,7,8,8,9,7,8,7,8,8,9,7,8,9,10,8,9,9,9,9,

%T 10,10,11,8,10,9,10,10,11,9,11,9,10,10,12,10,11,11,12,10,11,9,10,9,10,

%U 10,11,10,10,12,10,11,12,11,11,11,12,13,14,9,11,11

%N Number of steps to reach 1 by iterating the alternating sum of divisors function A071324 starting from n.

%H Amiram Eldar, <a href="/A333262/b333262.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 0 if n = 1 and a(n) = a(A071324(n)) + 1 otherwise.

%e a(3) = 2 since it takes 2 iterations of A071324 to reach from 3 to 1: 3 -> 2 -> 1.

%t f[n_] := Plus @@ (-(d = Divisors[n])*(-1)^(Range[Length[d],1,-1])); a[n_] := Length @ FixedPointList[f,n] - 2; Array[a, 100]

%Y Cf. A071324, A330786.

%K nonn

%O 1,3

%A _Amiram Eldar_, Mar 13 2020