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

Author

Amiram Eldar, Nov 06 2021

Keywords

• nonn

Comments

First differs from A348965 at n = 13.

All squarefree numbers are exponential unitary harmonic numbers.

Examples

			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.
		

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.

Crossrefs

Intersection of A013929 and A349026.

Cf. A005117, A348965.

Programs

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[#] &]