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A061283
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Smallest number with exactly 2n-1 divisors.
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14
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1, 4, 16, 64, 36, 1024, 4096, 144, 65536, 262144, 576, 4194304, 1296, 900, 268435456, 1073741824, 9216, 5184, 68719476736, 36864, 1099511627776, 4398046511104, 3600, 70368744177664, 46656, 589824, 4503599627370496, 82944
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OFFSET
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1,2
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COMMENTS
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The terms are always squares (because the divisors of a nonsquare N come in pairs, d and N/d, and so their number is always even - N. J. A. Sloane, Dec 26 2018).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000 (using A005179)
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FORMULA
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a(n) = Min{k | A000005(k)=2n-1}.
a(p) = 2^(p-1) for prime p.
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EXAMPLE
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For n=15, a(15)=144 with 15 divisors: {1,2,3,4,6,8,9,12...}.
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MATHEMATICA
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mp[1, m_] := {{}}; mp[n_, 1] := {{}}; mp[n_?PrimeQ, m_] := If[m < n, {}, {{n}}]; mp[n_, m_] := Join @@ Table[Map[Prepend[#, d] &, mp[n/d, d]], {d, Select[Rest[Divisors[n]], # <= m &]}]; mp[n_] := mp[n, n]; Table[mulpar = mp[2*n-1] - 1; Min[Table[Product[Prime[s]^mulpar[[j, s]], {s, 1, Length[mulpar[[j]]]}], {j, 1, Length[mulpar]}]], {n, 1, 100}] (* Vaclav Kotesovec, Apr 04 2021 *)
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CROSSREFS
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Cf. A000005, A000290, A005408, A003680, A016017, A037992, A055079, A048691.
Second bisection of A005179.
Sequence in context: A162547 A073533 A330689 * A242354 A001264 A307138
Adjacent sequences: A061280 A061281 A061282 * A061284 A061285 A061286
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KEYWORD
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nonn,changed
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AUTHOR
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Labos Elemer, May 22 2001
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STATUS
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approved
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