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A349025
a(n) is multiplicative with a(p^e) = Sum_{d||e} p^(e-d), where d||e are the unitary divisors of e.
2
1, 1, 1, 3, 1, 1, 1, 5, 4, 1, 1, 3, 1, 1, 1, 9, 1, 4, 1, 3, 1, 1, 1, 5, 6, 1, 10, 3, 1, 1, 1, 17, 1, 1, 1, 12, 1, 1, 1, 5, 1, 1, 1, 3, 4, 1, 1, 9, 8, 6, 1, 3, 1, 10, 1, 5, 1, 1, 1, 3, 1, 1, 4, 57, 1, 1, 1, 3, 1, 1, 1, 20, 1, 1, 6, 3, 1, 1, 1, 9, 28, 1, 1, 3, 1
OFFSET
1,4
COMMENTS
First differs from A348963 at n = 16.
A number k is an exponential unitary harmonic number (A349026) if and only if a(k) | k * A278908(k).
LINKS
Nicuşor Minculete, Contribuţii la studiul proprietăţilor analitice ale funcţiilor aritmetice - Utilizarea e-divizorilor, Ph.D. thesis, Academia Română, 2012. See section 4.3, pp. 90-94.
FORMULA
a(n) = 1 if and only if n is squarefree (A005117).
MATHEMATICA
f[p_, e_] := DivisorSum[e, p^(e - #) &, CoprimeQ[#, e/#] &]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
CROSSREFS
The unitary version of A348963.
Sequence in context: A369180 A351565 A254101 * A348963 A350470 A277604
KEYWORD
nonn,mult
AUTHOR
Amiram Eldar, Nov 06 2021
STATUS
approved