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A143700 a(n) is the least odd number m minimizing A007947(m*(2^n-m)). 8

%I

%S 1,1,1,1,5,1,3,13,169,25,243,375,11,49,7,3,18225,71875,4913,1701,

%T 144027,1825,3483,2197,9156027,131989,1103,5103,38525,458703,1523,

%U 3483891,19283525

%N a(n) is the least odd number m minimizing A007947(m*(2^n-m)).

%C Smallest odd number a(n) such that product of distinct prime divisors of (2^n)*a(n)*(2^n - a(n)) is the smallest available for a(n) <= 2^x - a(n) < 2^x.

%C Product of distinct prime divisors of (2^n)*a(n)*(2^n - a(n)) is also called radical: rad((2^n)*a(n)*(2^n - a(n))).

%C For numbers 2^n - a(n) see A143701.

%C For minimal values of rad((2^n)*a(n)*(2^n - a(n))) see A143702.

%C Related to the abc conjecture. - _M. F. Hasler_, Nov 13 2008

%t a = {{1, 1}}; aa = {1}; bb = {}; 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}]; aa (* _Artur Jasinski_ with assistance of _M. F. Hasler_ *)

%o (PARI) A143700(n) = {my(b=1, m=2^n-b); forstep(a=3, 2^(n-1), 2, A007947(a)*A007947(2^n-a)<m || next; m=A007947((2^n-a)*b=a)); b; } \\ _M. F. Hasler_, Nov 13 2008

%Y Cf. A007947, A085152, A085153, A147298-A147307, A147638-A147643.

%K nonn,more

%O 1,5

%A _Artur Jasinski_, Nov 10 2008

%E a(28)-a(33) from _M. F. Hasler_, Nov 13 2008

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Last modified April 17 23:03 EDT 2021. Contains 343071 sequences. (Running on oeis4.)