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Search: id:A094372
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| A094372 |
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Denominators of incrementally smallest ratios A002034(n)/n. |
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+0
5
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| 1, 2, 3, 4, 6, 8, 12, 40, 15, 16, 24, 30, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 252, 280, 360, 420, 504, 560, 720, 840, 1008, 1260, 1344, 1440, 1680, 1920, 2016, 2520, 2688, 2880, 3360, 3456, 4032, 5040, 5760, 6720, 8064, 8640, 10080, 10368, 11340, 13440, 72576, 15120, 17280, 20160, 22680, 24192, 25920, 26880, 30240
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Numerators are in A094404. Same as A094371(n)/gcd(A094371(n), A002034(A094371(n))). The factorials appear to form a subsequence.
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LINKS
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Eric Weisstein's World of Mathematics, Smarandache Function
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EXAMPLE
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a(5) = 6 because the 5th incrementally smallest ratio Smarandache(n)/n is 4/24 = 1/6.
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MATHEMATICA
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(Smarandache[n_] := (m = 1; While[ !IntegerQ[m!/n], m++ ]; m); M = {}; Do[With[{s = Smarandache[n]}, If[s/n < Min[M], M = Append[M, s/n]]], {n, 120}]; Denominator[M])
Smarandache[1] := 1; Smarandache[n_] := Max[Smarandache @@@ FactorInteger[n]]; Smarandache[p_, 1] := p; Smarandache[p_, alpha_] := Smarandache[p, alpha] = Module[{a, k, r, i, nu, k0 = alpha(p - 1)}, i = nu = Floor[Log[p, 1 + k0]]; a[1] = 1; a[n_] := (p^n - 1)/(p - 1); k[nu] = Quotient[alpha, a[nu]]; r[nu] = alpha - k[nu]a[nu]; While[r[i] > 0, k[i - 1] = Quotient[r[i], a[i - 1]]; r[i - 1] = r[i] - k[i - 1]a[i - 1]; i-- ]; k0 + Plus @@ k /@ Range[i, nu]]; M = {}; a = 2; Do[ s = Smarandache[n]; If[s/n < a, a = s/n; AppendTo[M, a]]], {n, 2, 40320}]; Denominator[M] (from EWW May 17 2004)
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CROSSREFS
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Cf. A002034, A094371, A094404, A094634.
Sequence in context: A161710 A018758 A068597 this_sequence A039880 A000029 A155051
Adjacent sequences: A094369 A094370 A094371 this_sequence A094373 A094374 A094375
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KEYWORD
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nonn,frac
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Apr 28 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 15 2004
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