A348215 a(n) is the sum of the iterated A348158 starting from n until a fixed point is reached.

0, 1, 0, 3, 0, 3, 0, 7, 0, 5, 0, 7, 0, 7, 0, 15, 0, 9, 0, 15, 0, 11, 0, 15, 0, 13, 0, 21, 0, 15, 0, 31, 0, 17, 0, 25, 0, 19, 0, 31, 0, 21, 0, 33, 0, 23, 0, 31, 0, 25, 0, 39, 0, 27, 0, 49, 0, 29, 0, 31, 0, 31, 57, 120, 0, 33, 0, 51, 0, 35, 0, 57, 0, 37, 0, 57

Offset: 1

Author

Amiram Eldar, Oct 07 2021

Keywords

• nonn

Comments

The first odd number k with a(k) > 0 is k = 63.

Examples

			a(4) = 3 since the iterations of the map x -> A348158(x) starting from 4 are 4 -> 3.
a(64) = 120 since the iterations of the map x -> A348158(x) starting from 64 are 64 -> 63 -> 57, and 63 + 57 = 120.
		

Links

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

Crossrefs

Cf. A092693, A326835, A348158, A348213, A348214.

Programs

Mathematica

f[n_] := Plus @@ DeleteDuplicates @ Map[EulerPhi, Divisors[n]]; a[n_] := Plus @@ Most @ FixedPointList[f, n] - n; Array[a, 100]

Formula

a(n) = 0 if and only if n is in A326835.

a(2*n) > 0 for all n.