cp's OEIS Frontend

A348697 Numbers m such that there are at least two smaller numbers k < m with the same harmonic mean of divisors as m.

%I A348697 #14 May 22 2025 23:18:13
%S A348697 321048,448335,1284192,1605240,1672125,1862190,3531528,5016375,
%T A348697 5457816,6420960,7384104,7621695,8026200,9310392,9952488,10311705,
%U A348697 11878776,13001715,13035330,13162968,13805064,13898385,14126112,15089256,16588395,17015544,17657640,17836000
%N A348697 Numbers m such that there are at least two smaller numbers k < m with the same harmonic mean of divisors as m.
%C A348697 What is the least term m with more than two smaller numbers k with the same harmonic mean of divisors as m?
%C A348697 The first such m is 44474832, which has harmonic mean of divisors 729/14, as do 5214132, 12553380 and 25676352. - _Robert Israel_, May 18 2025
%H A348697 Robert Israel, <a href="/A348697/b348697.txt">Table of n, a(n) for n = 1..101</a>
%e A348697 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.
%p A348697 hmd:= proc(n) local d,D;
%p A348697   D:= numtheory:-divisors(n);
%p A348697   nops(D)/add(1/d, d = D)
%p A348697 end proc:
%p A348697 R:= NULL: count:= 0:
%p A348697 for m from 1 while count < 50 do
%p A348697   v:= hmd(m);
%p A348697   if assigned(C[v]) then
%p A348697     C[v]:= C[v]+1;
%p A348697     if C[v] >= 3 then
%p A348697       R:= R,m; count:= count+1;
%p A348697     fi
%p A348697   else C[v]:= 1
%p A348697   fi;
%p A348697 od:
%p A348697 R; # _Robert Israel_, May 18 2025
%t A348697 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
%Y A348697 Cf. A099377, A099378, A348696.
%K A348697 nonn
%O A348697 1,1
%A A348697 _Amiram Eldar_, Oct 30 2021