OFFSET
1,2
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
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.
EXAMPLE
The squarefree numbers are trivial terms. If k is squarefree, then it has a single exponential unitary divisor, k itself, and thus the harmonic mean of its exponential unitary divisors is also k, which is an integer.
144 is a term since its exponential unitary divisors are 6, 18, 48 and 144, and their harmonic mean, 16, is an integer.
MATHEMATICA
f[p_, e_] := p^e * 2^PrimeNu[e] / DivisorSum[e, p^(e - #) &, CoprimeQ[#, e/#] &]; euhQ[1] = True; euhQ[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[100], euhQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 06 2021
STATUS
approved