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%I #19 Aug 12 2020 12:01:00
%S 1,3,7,15,27,63,125,243,343,999,1805,3721,8181,16335,32761,65533,
%T 112847,190269,519375,1046875,1953125,4192479,8385125,16775019,
%U 24398405,66976875,134216625
%N a(n) is the least odd number 2^n - m minimizing A007947(m*(2^n - m)).
%C 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.
%C The product of distinct prime divisors of m*(2^n-m) is also called the radical of that number: rad(m*(2^n-m)).
%F a(n) = 2^n - A143700(n).
%t 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_ *)
%Y Cf. A007947, A085152, A085153.
%Y Cf. A147298, A147299, A147300, A147302, A147303, A147305, A147306, A147307.
%Y Cf. A147638, A147639, A147640, A147641, A147642, A147643.
%K nonn,more
%O 1,2
%A _Artur Jasinski_, Nov 10 2008
%E a(1) added by _Jinyuan Wang_, Aug 11 2020
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