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

1,3

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A071324, A330786.

Sequence in context: A360746 A374066 A056791 * A218767 A334863 A329202

Adjacent sequences: A333259 A333260 A333261 * A333263 A333264 A333265

Keyword

nonn

Author

Amiram Eldar, Mar 13 2020

Status

approved