A348965 Exponential harmonic numbers of type 2 that are not squarefree.

12, 18, 36, 40, 60, 75, 84, 90, 120, 126, 132, 135, 150, 156, 180, 198, 204, 208, 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, 624, 630, 636, 660, 666, 675

Offset

1,1

Comments

Sándor (2006) proved that all squarefree numbers are exponential harmonic numbers of type 2.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

József Sándor, On exponentially harmonic numbers, Scientia Magna, Vol. 2, No. 3 (2006), pp. 44-47.

József Sándor, Selected Chapters of Geomety, Analysis and Number Theory, 2005, pp. 141-145.

Example

12 = 2^2 * 3 is a term since it is not squarefree, its exponential divisors are 6 and 12, and their harmonic mean, 8, is an integer.

Mathematica

f[p_, e_] := p^e * DivisorSigma[0, e] / DivisorSum[e, p^(e-#) &]; ehQ[1] = True; ehQ[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[1000], ! SquareFreeQ[#] && ehQ[#] &]

Crossrefs

Intersection of A013929 and A348964.

Cf. A005117, A348962.

Sequence in context: A079479 A293692 A349027 * A162694 A230354 A349180

Adjacent sequences: A348962 A348963 A348964 * A348966 A348967 A348968

Keyword

nonn

Author

Amiram Eldar, Nov 05 2021

Status

approved