A348918 Noninfinitary harmonic numbers: numbers such that the harmonic mean of their noninfinitary divisors is an integer.

4, 9, 12, 18, 25, 45, 49, 60, 96, 112, 121, 126, 150, 169, 289, 294, 336, 361, 448, 486, 529, 540, 560, 600, 637, 672, 726, 841, 961, 1014, 1232, 1344, 1350, 1369, 1638, 1680, 1681, 1734, 1849, 2166, 2209, 2430, 2809, 2850, 3174, 3481, 3721, 3822, 4200, 4320, 4489

Offset: 1

Author

Amiram Eldar, Nov 04 2021

Keywords

• nonn

Comments

Includes all the squares of primes (A001248), since they are the numbers with a single noninfinitary divisor.

Examples

			12 is a term since its noninfinitary divisors are {2, 6}, and their harmonic mean, 3, is an integer.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001248, A001599, A006086, A063947, A286325, A319745.

Programs

Mathematica

nidiv[1] = {}; nidiv[n_] := Complement[Divisors[n], Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; Select[Range[5000], (d = nidiv[#]) != {} && IntegerQ@ HarmonicMean[d] &]