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 A348694 a(n) is the least number k such that the numerator of the harmonic mean of the divisors of k is equal to n, or -1 if no such k exists. 2

%I #13 Oct 30 2021 10:41:35

%S 1,6,3,2,5,270,7,672,84,30,11,4,13,18620,420,24,17,12,19,10,21,22,23,

%T 30240,1550,78,9,168,29,60,31,8,132,102,35,18,37,38,39,3360,41,3724,

%U 43,7392,45,15456,47,1080,49,6051500,153,26,53,540,55,56,57,174,59,90

%N a(n) is the least number k such that the numerator of the harmonic mean of the divisors of k is equal to n, or -1 if no such k exists.

%H Amiram Eldar, <a href="/A348694/b348694.txt">Table of n, a(n) for n = 1..179</a>

%H Amiram Eldar, <a href="/A348694/a348694.txt">Table of n, a(n) for n = 1..1000 with 9 holes marked with 0</a>

%e a(2) = 6 since the harmonic mean of the divisors of 6 is 2.

%e a(3) = 3 since the harmonic mean of the divisors of 3 is 3/2.

%t num[n_] := Numerator[DivisorSigma[0, n]/DivisorSigma[-1, n]]; seq[m_] := Module[{s = Table[0, {m}], c = 0, n = 1, i}, While[c < m, i = num[n]; If[i <= m && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[100]

%Y Cf. A099377, A099378, A348695.

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 30 2021

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