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

1,3

Comments

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

Apparently, all the terms are odd.

Links

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

Formula

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

Example

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.

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]

Prog

(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

Crossrefs

Cf. A000010, A102190, A319696, A326835.

Sequence in context: A335115 A299149 A096866 * A360469 A320045 A334481

Adjacent sequences: A348155 A348156 A348157 * A348159 A348160 A348161

Keyword

nonn

Author

Amiram Eldar, Oct 03 2021

Status

approved