A348173 a(n) is the sum of the distinct values obtained when the unitary totient function is applied to the unitary divisors of n.

1, 1, 3, 4, 5, 3, 7, 8, 9, 5, 11, 12, 13, 7, 15, 16, 17, 9, 19, 20, 21, 11, 23, 24, 25, 13, 27, 28, 29, 15, 31, 32, 33, 17, 35, 36, 37, 19, 39, 40, 41, 21, 43, 44, 45, 23, 47, 48, 49, 25, 51, 52, 53, 27, 55, 56, 57, 29, 59, 60, 61, 31, 63, 64, 65, 33, 67, 68, 69, 35, 71, 72, 73, 37, 75, 76, 77, 39, 79, 80, 81, 41, 83, 78

Offset: 1

Author

Amiram Eldar, Oct 04 2021

Keywords

• nonn

Comments

First differs from A283971 at n = 84.

Examples

			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.
		

Links

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

Crossrefs

The unitary version of A348158.

Cf. A047994, A077610, A283971, A348001, A348004.

Programs

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]

Formula

a(n) <= n, with equality if and only if n is in A348004.