OFFSET
1,3
COMMENTS
First differs from A283971 at n = 84.
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 A348004.
EXAMPLE
The unitary divisors of 18 are {1, 2, 9, 18} and their uphi values are {1, 1, 8, 8}. The set of distinct values is {1, 8} whose sum is 9. Therefore, a(18) = 9.
MATHEMATICA
f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := Plus@@ DeleteDuplicates[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]; Array[a, 100]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 04 2021
STATUS
approved