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The least number k whose standard deviation of its prime factors (rounded up if necessary), with each factor counted according to its frequency of occurrence in the prime factorization of k (A067631) is n.
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%I #2 Mar 30 2012 17:30:42

%S 2,6,10,21,14,44,22,39,26,68,51,34,38,115,69,46,116,124,87,58,93,62,

%T 246,164,111,74,188,123,82,86,235,141,94,236,244,159,106,402,268,632,

%U 118,183,122,1068,316,201,134,332,213,142,146,553,395,856,158,388,904

%N The least number k whose standard deviation of its prime factors (rounded up if necessary), with each factor counted according to its frequency of occurrence in the prime factorization of k (A067631) is n.

%e a(16) = 116 because 116 = 2*2*29, their Standard Deviation is 9*Sqrt(3) which equals approximately 15.5885 and when rounded up equals 16.

%t Needs[ "Statistics`NormalDistribution`" ]; f[n_Integer] := Module[ {a = FactorInteger[n], b = {}}, While[ Length[a] > 0, Do[b = Append[b, a[[1, 1]]], {a[[1, 2]]}]; a = Drop[a, 1]]; b]; g[n_] := If[ PrimeQ[n], Return[0], Floor[ StandardDeviation[ f[n]] + 0.5]]; a = Table[0, {100}]; Do[b = g[n]; If[b < 100 && a[[b + 1]] == 0, a[[b + 1]] = n], {n, 101, 10^4}]; a

%Y Cf. A067631.

%K easy,nonn

%O 0,1

%A _Robert G. Wilson v_, Feb 05 2002