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.

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

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, A147298-A147307.

Sequence in context: A029167 A161103 A337879 * A108380 A361231 A377281

Adjacent sequences: A147298 A147299 A147300 * A147302 A147303 A147304

Keyword

nonn

Author

Artur Jasinski, Nov 05 2008

Status

approved