login
A349027
Exponential unitary harmonic numbers (A349026) that are not squarefree.
2
12, 18, 36, 40, 60, 75, 84, 90, 120, 126, 132, 135, 144, 150, 156, 180, 198, 204, 228, 234, 252, 270, 276, 280, 306, 342, 348, 360, 372, 396, 414, 420, 440, 444, 450, 468, 492, 516, 520, 522, 525, 540, 544, 558, 564, 588, 600, 612, 630, 636, 660, 666, 675, 680
OFFSET
1,1
COMMENTS
First differs from A348965 at n = 13.
All squarefree numbers are exponential unitary harmonic numbers.
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.
EXAMPLE
12 = 2^2 * 3 is a term since it is not squarefree, its exponential unitary divisors are 6 and 12, and their harmonic mean, 8, 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[1000], ! SquareFreeQ[#] && euhQ[#] &]
CROSSREFS
Intersection of A013929 and A349026.
Sequence in context: A319746 A079479 A293692 * A348965 A162694 A230354
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 06 2021
STATUS
approved