A348697 Numbers m such that there are at least two smaller numbers k < m with the same harmonic mean of divisors as m.
321048, 448335, 1284192, 1605240, 1672125, 1862190, 3531528, 5016375, 5457816, 6420960, 7384104, 7621695, 8026200, 9310392, 9952488, 10311705, 11878776, 13001715, 13035330, 13162968, 13805064, 13898385, 14126112, 15089256, 16588395, 17015544, 17657640, 17836000
Offset: 1
Keywords
Examples
321048 is a term since the harmonic mean of divisors of 321048 is 3528/125, and it is also the harmonic mean of divisors of both 201096 and 296352 which are smaller than 321048.
Links
- Robert Israel, Table of n, a(n) for n = 1..101
Programs
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Maple
hmd:= proc(n) local d,D; D:= numtheory:-divisors(n); nops(D)/add(1/d, d = D) end proc: R:= NULL: count:= 0: for m from 1 while count < 50 do v:= hmd(m); if assigned(C[v]) then C[v]:= C[v]+1; if C[v] >= 3 then R:= R,m; count:= count+1; fi else C[v]:= 1 fi; od: R; # Robert Israel, May 18 2025 -
Mathematica
h = Table[DivisorSigma[0, n]/DivisorSigma[-1, n], {n, 1, 2*10^6}]; i = Position[(t = Tally[h])[[;; , 2]], _?(# > 2 &)] // Flatten; Position[h, #][[3 ;; -1]] & /@ t[[i, 1]] // Flatten // Sort
Comments