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

KEYWORD

nonn

AUTHOR

Amiram Eldar, Oct 03 2021

STATUS

approved