Search: id:A094372
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%I A094372
%S A094372 1,2,3,4,6,8,12,40,15,16,24,30,40,45,48,60,72,80,90,120,144,180,240,252,
%T A094372 280,360,420,504,560,720,840,1008,1260,1344,1440,1680,1920,2016,2520,
%U A094372 2688,2880,3360,3456,4032,5040,5760,6720,8064,8640,10080,10368,11340,13440,
               72576,15120,17280,20160,22680,24192,25920,26880,30240
%N A094372 Denominators of incrementally smallest ratios A002034(n)/n.
%C A094372 Numerators are in A094404. Same as A094371(n)/gcd(A094371(n), A002034(A094371(n))). 
               The factorials appear to form a subsequence.
%H A094372 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SmarandacheFunction.html">Smarandache Function</a>
%e A094372 a(5) = 6 because the 5th incrementally smallest ratio Smarandache(n)/
               n is 4/24 = 1/6.
%t A094372 (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])
%t A094372 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)
%Y A094372 Cf. A002034, A094371, A094404, A094634.
%Y A094372 Sequence in context: A161710 A018758 A068597 this_sequence A039880 A000029 
               A155051
%Y A094372 Adjacent sequences: A094369 A094370 A094371 this_sequence A094373 A094374 
               A094375
%K A094372 nonn,frac
%O A094372 1,2
%A A094372 Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Apr 28 2004
%E A094372 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 15 2004

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