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%I #7 Nov 08 2017 12:11:09
%S 1,1,1,2,1,2,3,2,3,5,5,6,3,2,5,7,7,6,7,10,7,10,11,11,11,13,13,14,13,
%T 14,15,14,15,13,17,15,17,17,19,19,19,21,21,22,17,21,19,23,21,22,23,23,
%U 23,26,23,26,23,29,29,30,29,29,31,31,31,33,33,34,33,34,35,35,35,37,37,38
%N a(n) = smallest value of parameter m such that the function rad(m n (n - m)) has maximal 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 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 biggest values of the function rad(m n (n - m)) see A147299.
%C For numbers m for which rad(m n (n - m)) reaches a minimal value see A147300.
%C For numbers m for which rad(m n (n - m)) reaches a maximal value see A147301.
%C For the sequence in each value log(n)/log(A147298(n)) reached 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}]; cc (* _Artur Jasinski_ *)
%Y Cf. A085152, A085153, A147298-A147307.
%K nonn
%O 2,4
%A _Artur Jasinski_, Nov 05 2008
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