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%I #11 Nov 08 2017 12:09:09
%S 2,6,6,30,30,70,30,42,210,330,210,546,462,390,110,1190,462,1482,910,
%T 2310,2310,2990,858,770,4290,546,2730,6090,6630,7378,510,8778,9690,
%U 10010,1938,12210,13566,14586,3990,17138,18354,19866,10626,7590,22678
%N a(n) = largest value of the function rad(m*n*(n - m)) 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 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 Sequence in which each value log(n)/log(A147298(n)) reaches records see A147302.
%H Ivan Neretin, <a href="/A147299/b147299.txt">Table of n, a(n) for n = 2..1000</a>
%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}]; bb (* _Artur Jasinski_ *)
%t Table[Max[Times @@ FactorInteger[#][[All, 1]] & /@ ((m = Range[1, n - 1])*(n - m)*n)], {n, 2, 46}] (* _Ivan Neretin_, May 21 2015 *)
%Y Cf. A085152, A085153, A147298-A147307.
%K nonn
%O 2,1
%A _Artur Jasinski_, Nov 05 2008
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