A147300 a(n) = smallest value of parameter m such that the function rad(m*n*(n - m)) has minimal 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, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 2, 1, 2, 1, 4, 5, 1, 9, 3, 1, 1, 11, 7, 1, 9, 1, 16, 1, 1, 1, 2, 1, 1, 1, 1, 25, 4, 5, 1, 1, 25, 9, 27, 1, 1, 1, 1, 1, 1, 1, 3, 1, 5, 1, 7, 1, 1, 25, 11, 1, 13, 1, 4, 1, 1, 1, 2, 1, 4, 5, 23, 7, 8, 1, 27, 11, 1, 13, 14, 1, 1, 17, 1, 1

Offset

2,10

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 the largest values of the function rad(m n (n - m)) see A147299.

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.

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

Links

Table of n, a(n) for n=2..100.

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}]; dd (* Artur Jasinski *)

Crossrefs

Cf. A085152, A085153, A147298-A147307.

Sequence in context: A177121 A329314 A092931 * A346481 A240228 A110503

Adjacent sequences: A147297 A147298 A147299 * A147301 A147302 A147303

Keyword

nonn

Author

Artur Jasinski, Nov 05 2008

Status

approved