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

1,4

Comments

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

Links

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

Formula

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

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A045763 A132748 A022901 * A331739 A356169 A055945

Adjacent sequences: A348212 A348213 A348214 * A348216 A348217 A348218

Keyword

nonn

Author

Amiram Eldar, Oct 07 2021

Status

approved