A349027 Exponential unitary harmonic numbers (A349026) that are not squarefree.

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

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

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.

Cf. A005117, A348965.

Sequence in context: A319746 A079479 A293692 * A348965 A162694 A230354

Adjacent sequences: A349024 A349025 A349026 * A349028 A349029 A349030

Keyword

nonn

Author

Amiram Eldar, Nov 06 2021

Status

approved