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A143701 a(n) = least odd number 2^n - m minimizing A007947(m*(2^n - m)). 4
3, 7, 15, 27, 63, 125, 243, 343, 999, 1805, 3721, 8181, 16335, 32761, 65533, 112847, 190269, 519375, 1046875, 1953125, 4192479, 8385125, 16775019, 24398405, 66976875, 134216625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 (2^n)*a(n)*(2^n-a(n)) is also called the radical of that number: rad((2^n)*a(n)*(2^n-a(n)).

For numbers 2^n-a(n) see A143701. [Wrong A-number? - N. J. A. Sloane, Nov 13 2008]

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

For minimal values of rad(a(n)*(2^n-a(n)) see A143703.

LINKS

Table of n, a(n) for n=1..26.

MATHEMATICA

a = {{1, 1}}; 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

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

Sequence in context: A146726 A146228 A139806 * A147638 A147394 A103021

Adjacent sequences:  A143698 A143699 A143700 * A143702 A143703 A143704

KEYWORD

nonn

AUTHOR

Artur Jasinski, Nov 10 2008

STATUS

approved

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Last modified November 14 15:00 EST 2019. Contains 329126 sequences. (Running on oeis4.)