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 A147298 Minimum of rad(m (n - m) n) for 0 < m < n, gcd(m,n) = 1, where rad(k) = A007947(k) = product of prime factors of k. 28
 2, 6, 6, 10, 30, 42, 14, 6, 30, 66, 66, 78, 182, 210, 30, 34, 102, 114, 190, 210, 462, 322, 138, 30, 130, 30, 42, 174, 870, 186, 30, 66, 510, 210, 210, 222, 1254, 546, 390, 246, 1722, 258, 946, 330, 690, 1410, 282, 42, 70, 510, 390, 742, 210, 330, 770, 570, 1218 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Function rad(k) is used in ABC conjecture applications. For biggest values of function rad(m n (n - m)) see A147299. For numbers m for which rad(m n (n - m)) reached minimal value see A147300. For numbers m for which rad(m n (n - m)) reached maximal value see A147301. Sequence in each value Log[n]/Log[A147298(n)] reached records see A147297. LINKS Ivan Neretin, Table of n, a(n) for n = 2..1000 MAPLE A147298 := proc(n) local rad, g, L; rad := n -> mul(k, k in numtheory:-factorset(n)): g := (n, k) -> `if`(igcd(n, k) = 1, 1, infinity): L := n -> [seq(g(n, k)*rad(n*k*(n-k)), k=1..n/2)]: min(L(n)) end: seq(A147298(n), n=2..58); # Peter Luschny, Aug 06 2019 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}]; aa (*Artur Jasinski*) Table[Min[Times @@ FactorInteger[#][[All, 1]] & /@ ((m = Select[Range[1, n - 1], GCD[n, #] == 1 &])*(n - m)*n)], {n, 2, 58}] (* Ivan Neretin, May 21 2015 *) PROG (PARI) A147298(n)= local(m=n^2); for( a=1, n\2, gcd(a, n)>1 && next; A007947(n-a)*A007947(a)

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Last modified December 9 17:12 EST 2022. Contains 358702 sequences. (Running on oeis4.)