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 A147300 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. 11
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,10 COMMENTS The function rad(k) is used in ABC conjecture applications. For smallest values of the function rad(m n (n - m)) see A147298. For the largest values of the function rad(m n (n - m)) see A147299. For numbers m at which rad(m*n*(n - m)) reaches minimal value see A147300. For numbers m at which rad(m*n*(n - m)) reaches maximal value see A147301. For sequence in which each value log(n)/log(A147298(n)) reaches records see A147302. LINKS MATHEMATICA 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 *) CROSSREFS Cf. A085152, A085153, A147298-A147307. Sequence in context: A177121 A329314 A092931 * A240228 A110503 A030556 Adjacent sequences:  A147297 A147298 A147299 * A147301 A147302 A147303 KEYWORD nonn AUTHOR Artur Jasinski, Nov 05 2008 STATUS approved

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Last modified October 1 15:05 EDT 2020. Contains 337443 sequences. (Running on oeis4.)