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%I #9 Nov 08 2017 12:10:19
%S 1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,2,1,2,1,4,5,1,9,3,
%T 1,1,11,7,1,9,1,16,1,1,1,2,1,1,1,1,25,4,5,1,1,25,9,27,1,1,1,1,1,1,1,3,
%U 1,5,1,7,1,1,25,11,1,13,1,4,1,1,1,2,1,4,5,23,7,8,1,27,11,1,13,14,1,1,17,1,1
%N a(n) = smallest value of parameter m such that the function rad(m*n*(n - m)) has minimal value n=2,3,4,..., 0 < m < n where the function rad(k) (also called radical(k)) is the product of distinct prime divisors of k.
%C The function rad(k) is used in ABC conjecture applications.
%C For smallest values of the function rad(m n (n - m)) see A147298.
%C For the largest values of the function rad(m n (n - m)) see A147299.
%C For numbers m at which rad(m*n*(n - m)) reaches minimal value see A147300.
%C For numbers m at which rad(m*n*(n - m)) reaches maximal value see A147301.
%C For sequence in which each value log(n)/log(A147298(n)) reaches records see A147302.
%t logmax = 0; aa = {}; bb = {}; cc = {}; dd = {}; ee = {}; ff = {}; gg \ = {}; Do[min = 10^100; max = 0; ile = 0; Do[If[GCD[m, n, n - m] == 1, ile = ile + 1; s = m n (n - m); k = FactorInteger[s]; g = 1; Do[g = g k[[p]][[1]], {p, 1, Length[k]}]; If[g > max, max = g; mmax = m]; If[g < min, min = g; mmin = m]], {m, 1, n - 1}]; AppendTo[aa, min]; AppendTo[bb, max]; AppendTo[cc, mmax]; AppendTo[dd, mmin]; AppendTo[gg, ile]; If[(Log[n]/Log[min]) > logmax, logmax = (Log[n]/Log[min]); AppendTo[ee, {N[logmax], n, mmin, min, mmax, max}]; Print[{N[logmax], n, mmin, min, mmax, max}]; AppendTo[ff, n]], {n, 2, 129}]; dd (* _Artur Jasinski_ *)
%Y Cf. A085152, A085153, A147298-A147307.
%K nonn
%O 2,10
%A _Artur Jasinski_, Nov 05 2008
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