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A291211 Numbers k>1 such that k*k^(1/k) is closer to an integer than for any smaller number.

%I A291211 #14 Aug 22 2017 20:16:14
%S A291211 2,5,6,15,16,46,135,136,385,1072,21976,59813,59814,162682,162683,
%T A291211 442329,1202506,3268905,24154808,65659807,485164995,1318815513,
%U A291211 1318815514,26489121842,72004899025,195729609091,532048240237,1446257063899
%N A291211 Numbers k>1 such that k*k^(1/k) is closer to an integer than for any smaller number.
%C A291211 The corresponding closest matching integers are given in A291212.
%e A291211 Let s(x) = x*x^(1/x), r(x) = round(s(x)), d(x) = abs(s(x)-r(x));
%e A291211 a(1) = 2:
%e A291211   s(2) = 2.8284271...,
%e A291211   r(2) = A291212(1) = 3,
%e A291211   d(2) = 0.17157...;
%e A291211 a(2) = 5:
%e A291211   s(5) = 6.8986483...,
%e A291211   r(5) = A291212(2) = 7,
%e A291211   d(5) = 0.10135169...;
%e A291211 a(3) = 6:
%e A291211   s(6) = 8.0880369...,
%e A291211   r(6) = A291212(3) = 8,
%e A291211   d(6) = 0.08803692...;
%e A291211 a(4) = 15:
%e A291211   s(15) = 17.96790087...,
%e A291211   r(15) = A291212(4) = 18,
%e A291211   d(18) = 0.03209912...;
%e A291211 a(5) = 16:
%e A291211   s(16) = 19.02731384...,
%e A291211   r(16) = A291212(5) = 19,
%e A291211   d(19) = 0.02731384...;
%Y A291211 Cf. A291210, A291212.
%K A291211 nonn
%O A291211 1,1
%A A291211 _Hugo Pfoertner_, Aug 21 2017