A333262 Number of steps to reach 1 by iterating the alternating sum of divisors function A071324 starting from n.

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, 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, 10, 11, 10, 10, 12, 10, 11, 12, 11, 11, 11, 12, 13, 14, 9, 11, 11

Offset: 1

Author

Amiram Eldar, Mar 13 2020

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071324, A330786.

Programs

Mathematica

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

Formula

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