Search: id:A078709
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%I A078709
%S A078709 1,1,1,1,2,1,3,2,3,2,5,2,6,3,3,3,8,3,9,3,5,5,11,3,8,6,6,4,14,3,15,5,8,
               8,
%T A078709 8,4,18,9,9,5,20,5,21,7,7,11,23,4,16,8,12,8,26,6,13,7,14,14,29,5,30,15,
%U A078709 10,9,16,8,33,11,17,8,35,6,36,18,12,12,19,9,39,8,16,20,41,7,21,21,21,11
%N A078709 Integer part of the mean subinterval length in the partition of [0,n] 
               by the divisors of n.
%C A078709 If the first occurrence of m in the sequence is greater than all preceding 
               terms, the corresponding n is non-composite. - Donald Sampson (Marsquo(AT)hotmail.com), 
               Dec 10 2003
%F A078709 a(n) = floor(n/tau(n)), where tau(n) is the number of divisors of n (A000005). 
               - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 26 2003
%e A078709 The divisors of 9 partition the closed interval [0,9] into subintervals 
               [0,1), [1,3), [3,9], with lengths 1, 2, 6, respectively. The mean 
               of these lengths has integer part = 3. Hence a(9) = 3.
%t A078709 << Statistics`DescriptiveStatistics` f[n_] := Module[{d, l, a, i}, d 
               = Divisors[n]; l = Length[d]; a = {1}; For[i = 1, i <= l - 1, i++, 
               a = Append[a, d[[i + 1]] - d[[i]]]]; a]; Table[Floor[Mean[f[i]]], 
               {i, 1, 100}]
%Y A078709 Cf. A078710.
%Y A078709 Sequence in context: A007828 A070804 A104481 this_sequence A023022 A100677 
               A083290
%Y A078709 Adjacent sequences: A078706 A078707 A078708 this_sequence A078710 A078711 
               A078712
%K A078709 nonn
%O A078709 1,5
%A A078709 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 19 2002

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