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.

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

Offset: 2

Author

Artur Jasinski, Nov 05 2008

Keywords

• nonn

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

Crossrefs

Cf. A085152, A085153, A147298-A147307.

Programs

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 *)