

A147301


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.


7



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, 14, 15, 14, 15, 13, 17, 15, 17, 17, 19, 19, 19, 21, 21, 22, 17, 21, 19, 23, 21, 22, 23, 23, 23, 26, 23, 26, 23, 29, 29, 30, 29, 29, 31, 31, 31, 33, 33, 34, 33, 34, 35, 35, 35, 37, 37, 38
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OFFSET

2,4


COMMENTS

Function rad(k) is used in ABC conjecture applications.
For smallest values of the function rad(m n (n  m)) see A147298.
For biggest values of the function rad(m n (n  m)) see A147299.
For numbers m for which rad(m n (n  m)) reaches a minimal value see A147300.
For numbers m for which rad(m n (n  m)) reaches a maximal value see A147301.
For the sequence in each value log(n)/log(A147298(n)) reached records see A147302.


LINKS

Table of n, a(n) for n=2..77.


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}]; cc (* Artur Jasinski *)


CROSSREFS

Cf. A085152, A085153, A147298A147307.
Sequence in context: A119994 A029167 A161103 * A108380 A302098 A112779
Adjacent sequences: A147298 A147299 A147300 * A147302 A147303 A147304


KEYWORD

nonn


AUTHOR

Artur Jasinski, Nov 05 2008


STATUS

approved



