login
a(n) is the sum of the distinct values obtained when the unitary totient function is applied to the unitary divisors of n.
3

%I #8 Oct 06 2021 02:53:52

%S 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,

%T 28,29,15,31,32,33,17,35,36,37,19,39,40,41,21,43,44,45,23,47,48,49,25,

%U 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

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

%C First differs from A283971 at n = 84.

%H Amiram Eldar, <a href="/A348173/b348173.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

%t 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]

%Y The unitary version of A348158.

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

%K nonn

%O 1,3

%A _Amiram Eldar_, Oct 04 2021