A348215 - OEIS

%I #10 Oct 09 2021 04:11:43

%S 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,

%T 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,

%U 0,31,0,31,57,120,0,33,0,51,0,35,0,57,0,37,0,57

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

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

%H Amiram Eldar, <a href="/A348215/b348215.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%e a(4) = 3 since the iterations of the map x -> A348158(x) starting from 4 are 4 -> 3.

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

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

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

%K nonn

%O 1,4

%A _Amiram Eldar_, Oct 07 2021