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%I #29 Jul 31 2017 05:57:35
%S 1,2,4,8,9,16,27,32,64,81,125,128,243,256,343,512,625,729,1024,2048,
%T 2187,2197,2401,3125,4096,4913,6561,6859,8192,12167,14641,15625,16384,
%U 16807,19683,24389,28561,29791,32768,50653,59049,65536,68921,78125,79507,83521
%N Consider the function f(k) in A110545, i.e., the smallest positive integer j such that k divides either the numerator or the denominator of the reduced Harmonic number H(j). This sequence lists numbers k where f(k)=k.
%C If p^e is present then p^(e+1) is also. The generators are: 2^0, 3^2, 5^3, 7^3, 11^4, 13^3, 17^3, 19^3, 23^3, 29^3, 31^3, ...
%C Conjecture: only prime powers are present (A025475) in addition to 1 and 2. Thus this sequence would be a proper subset of A000961.
%H Robert G. Wilson v, <a href="/A113570/b113570.txt">Table of n, a(n) for n = 1..57</a>
%t f[n_] := Block[{h = k = 1}, While[ !IntegerQ[ Numerator[h]/n] && !IntegerQ[ Denominator[h]/n], k++; h = h + 1/k]; k]; t = Table[f[n], {n, 10000}]; Select[ Range[10000], t[[ # ]] == # &]
%Y Cf. A110545.
%K nonn
%O 1,2
%A _Leroy Quet_ and _Robert G. Wilson v_, Sep 29 2005
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