A348158 a(n) is the sum of the distinct values obtained when the Euler totient function is applied to the divisors of n.

1, 1, 3, 3, 5, 3, 7, 7, 9, 5, 11, 7, 13, 7, 15, 15, 17, 9, 19, 15, 21, 11, 23, 15, 25, 13, 27, 21, 29, 15, 31, 31, 33, 17, 35, 25, 37, 19, 39, 31, 41, 21, 43, 33, 45, 23, 47, 31, 49, 25, 51, 39, 53, 27, 55, 49, 57, 29, 59, 31, 61, 31, 57, 63, 65, 33, 67, 51, 69

Offset: 1

Author

Amiram Eldar, Oct 03 2021

Keywords

• nonn

Comments

The sum of the distinct values of the n-th row of A102190.

Apparently, all the terms are odd.

Examples

			The divisors of 12 are {1, 2, 3, 4, 6, 12} and their phi values are {1, 1, 2, 2, 2, 4}. The set of distinct values is {1, 2, 4} whose sum is 7. Therefore, a(12) = 7.
		

Links

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

Crossrefs

Cf. A000010, A102190, A319696, A326835.

Programs

Maple

with(numtheory):
a:= n-> add(i, i=map(phi, divisors(n))):
seq(a(n), n=1..69);  # Alois P. Heinz, Nov 15 2021

Mathematica

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

PARI

a(n) = vecsum(Set(apply(eulerphi, divisors(n)))); \\ Michel Marcus, Oct 04 2021

Python

from sympy import totient, divisors
def A348158(n): return sum(set(map(totient,divisors(n,generator=True)))) # Chai Wah Wu, Nov 15 2021

Formula

a(n) <= n, with equality if and only if n is in A326835.