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

1,1

Comments

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

Links

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

Example

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

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] &]

Crossrefs

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

Sequence in context: A357497 A319745 A312865 * A181023 A084789 A157650

Adjacent sequences: A348915 A348916 A348917 * A348919 A348920 A348921

Keyword

nonn

Author

Amiram Eldar, Nov 04 2021

Status

approved