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Search: id:A143701
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| A143701 |
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a(n) = least odd number 2^n-m minimizing A007947(m(2^n-m)) |
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+0
4
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
Product of distinct prime divisors of (2^n)*a(n)*(2^n-a(n)) is called also radical: rad((2^n)*a(n)*(2^n-a(n))
For numbers 2^n-a(n) see A143701 [Wrong A-number? - N. J. A. Sloane (njas(AT)research.att.com), 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
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MATHEMATICA
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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 Maximilian Hasler*)
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CROSSREFS
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Cf. A007947, A085152, A085153, A147298-A147307, A147638-A147643.
Sequence in context: A146726 A146228 A139806 this_sequence A147638 A147394 A103021
Adjacent sequences: A143698 A143699 A143700 this_sequence A143702 A143703 A143704
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Nov 10 2008
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