%I #22 Nov 05 2021 14:33:34

%S 4,9,12,18,25,45,49,60,96,112,121,126,150,169,289,294,336,361,448,486,

%T 529,540,560,600,637,672,726,841,961,1014,1232,1344,1350,1369,1638,

%U 1680,1681,1734,1849,2166,2209,2430,2809,2850,3174,3481,3721,3822,4200,4320,4489

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

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

%H Amiram Eldar, <a href="/A348918/b348918.txt">Table of n, a(n) for n = 1..5000</a>

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

%t 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] &]

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

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 04 2021