OFFSET
1,2
COMMENTS
a(n) is the smallest odd number such that the product of distinct prime divisors of (2^n)*a(n)*(2^n-a(n)) is the smallest for the range a(n) <= 2^x - a(n) < 2^x.
The product of distinct prime divisors of m*(2^n-m) is also called the radical of that number: rad(m*(2^n-m)).
FORMULA
a(n) = 2^n - A143700(n).
MATHEMATICA
aa = {1}; bb = {1}; rr = {}; Do[logmax = 0; k = 2^x; w = Floor[(k - 1)/2]; Do[m = FactorInteger[n (k - n)]; rad = 1; Do[rad = rad m[[s]][[1]], {s, 1, Length[m]}]; log = Log[k]/Log[rad]; If[log > logmax, bmin = k - n; amax = n; logmax = log; r = rad], {n, 1, w, 2}]; Print[{x, amax}]; AppendTo[aa, amax]; AppendTo[bb, bmin]; AppendTo[rr, r]; AppendTo[a, {x, logmax}], {x, 2, 15}]; bb (* Artur Jasinski with assistance of M. F. Hasler *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Artur Jasinski, Nov 10 2008
EXTENSIONS
a(1) added by Jinyuan Wang, Aug 11 2020
STATUS
approved