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A348001 Number of distinct values obtained when the unitary totient function (A047994) is applied to the unitary divisors of n.

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%I A348001 #9 Sep 25 2021 04:45:24
%S A348001 1,1,2,2,2,2,2,2,2,2,2,4,2,2,4,2,2,2,2,4,4,2,2,4,2,2,2,4,2,4,2,2,4,2,
%T A348001 4,4,2,2,4,4,2,4,2,4,4,2,2,4,2,2,4,4,2,2,4,4,4,2,2,8,2,2,4,2,4,4,2,4,
%U A348001 4,4,2,4,2,2,4,4,4,4,2,4,2,2,2,7,4,2,4
%N A348001 Number of distinct values obtained when the unitary totient function (A047994) is applied to the unitary divisors of n.
%H A348001 Amiram Eldar, <a href="/A348001/b348001.txt">Table of n, a(n) for n = 1..10000</a>
%F A348001 a(2^e) = 2 for e > 1.
%F A348001 a(p^e) = 2 for an odd prime p and e > 0.
%F A348001 a(n) >= omega(n), with equality if and only if n is in A278568.
%e A348001 n = 6 has four unitary divisors: 1, 2, 3 and 6. Applying A047994 to these gives 1, 1, 2 and 2, with just 2 distinct values, thus a(6) = 2.
%e A348001 n = 12 has four unitary divisors: 1, 3, 4 and 12. Applying A047994 to these gives 4 distinct values, 1, 2, 3 and 6, thus a(12) = 4.
%t A348001 f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := Length @ Union[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]; Array[a,100]
%Y A348001 The unitary version of A319696.
%Y A348001 Cf. A047994, A077610, A278568.
%K A348001 nonn
%O A348001 1,3
%A A348001 _Amiram Eldar_, Sep 23 2021