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A348918
Noninfinitary harmonic numbers: numbers such that the harmonic mean of their noninfinitary divisors is an integer.
2
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 04 2021
STATUS
approved