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A147299 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. 9
2, 6, 6, 30, 30, 70, 30, 42, 210, 330, 210, 546, 462, 390, 110, 1190, 462, 1482, 910, 2310, 2310, 2990, 858, 770, 4290, 546, 2730, 6090, 6630, 7378, 510, 8778, 9690, 10010, 1938, 12210, 13566, 14586, 3990, 17138, 18354, 19866, 10626, 7590, 22678 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

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 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.

Sequence in which each value log(n)/log(A147298(n)) reaches records see A147302.

LINKS

Ivan Neretin, Table of n, a(n) for n = 2..1000

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}]; bb (* Artur Jasinski *)

Table[Max[Times @@ FactorInteger[#][[All, 1]] & /@ ((m = Range[1, n - 1])*(n - m)*n)], {n, 2, 46}] (* Ivan Neretin, May 21 2015 *)

CROSSREFS

Cf. A085152, A085153, A147298-A147307.

Sequence in context: A056040 A333073 A099566 * A090549 A080326 A034386

Adjacent sequences:  A147296 A147297 A147298 * A147300 A147301 A147302

KEYWORD

nonn

AUTHOR

Artur Jasinski, Nov 05 2008

STATUS

approved

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Last modified September 24 11:11 EDT 2020. Contains 337317 sequences. (Running on oeis4.)