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A147300
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a(n) = smallest value of parameter m such that function rad(m n (n - m)) have minimal value n=2,3,4..., 0 < m < n where function rad(k) called also radical(k) is product distinct prime divisors of k.
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10
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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; internal format)
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OFFSET
| 2,10
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COMMENTS
| Function rad(k) is used in ABC conjecture applications.
For smallest values of function rad(m n (n - m)) see A147298
For biggest values of function rad(m n (n - m)) see A147299
For numbers m for which rad(m n (n - m)) reached minimal value see A147300
For numbers m for which rad(m n (n - m)) reached maximal value see A147301
Sequence in each value Log[n]/Log[A147298(n)] reached records see A147302
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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*)
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CROSSREFS
| A085152, A085153, A147298-A147307.
Sequence in context: A086251 A177121 A092931 * A110503 A030556 A030575
Adjacent sequences: A147297 A147298 A147299 * A147301 A147302 A147303
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Nov 05 2008
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