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A348001
Number of distinct values obtained when the unitary totient function (A047994) is applied to the unitary divisors of n.
6
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, 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, 4, 4, 2, 4, 2, 2, 4, 4, 4, 4, 2, 4, 2, 2, 2, 7, 4, 2, 4
OFFSET
1,3
LINKS
FORMULA
a(2^e) = 2 for e > 1.
a(p^e) = 2 for an odd prime p and e > 0.
a(n) >= omega(n), with equality if and only if n is in A278568.
EXAMPLE
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.
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.
MATHEMATICA
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]
CROSSREFS
The unitary version of A319696.
Sequence in context: A343336 A103817 A073808 * A361923 A032572 A237975
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 23 2021
STATUS
approved