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A348158
a(n) is the sum of the distinct values obtained when the Euler totient function is applied to the divisors of n.
9
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
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