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Search: id:A147298
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| A147298 |
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Minimum of rad(m (n - m) n) for 0 < m < n, gcd(m,n) = 1, where rad(k) = A007947(k) = product of prime factors of k. |
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26
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| 2, 6, 6, 10, 30, 42, 14, 6, 30, 66, 66, 78, 182, 210, 30, 34, 102, 114, 190, 210, 462, 322, 138, 30, 130, 30, 42, 174, 870, 186, 30, 66, 510, 210, 210, 222, 1254, 546, 390, 246, 1722, 258, 946, 330, 690, 1410, 282, 42, 70, 510, 390, 742, 210, 330, 770, 570, 1218
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Function rad(k) is used in ABC conjecture applications.
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 A147297
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MATHEMATICA
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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}]; aa (*Artur Jasinski*)
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PROGRAM
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(PARI) A147298(n)={ local(m=n^2); for( a=1, n\2, gcd(a, n)>1 & next; A007947(n-a)*A007947(a)<m | next; m=A007947(n-a)*A007947(a)); m*A007947(n) }
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CROSSREFS
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Cf. A007947, A085152, A085153, A147298-A147307.
Sequence in context: A063210 A114718 A102261 this_sequence A078636 A083482 A099027
Adjacent sequences: A147295 A147296 A147297 this_sequence A147299 A147300 A147301
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Nov 05 2008
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