A067716 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.

2, 6, 10, 21, 14, 44, 22, 39, 26, 68, 51, 34, 38, 115, 69, 46, 116, 124, 87, 58, 93, 62, 246, 164, 111, 74, 188, 123, 82, 86, 235, 141, 94, 236, 244, 159, 106, 402, 268, 632, 118, 183, 122, 1068, 316, 201, 134, 332, 213, 142, 146, 553, 395, 856, 158, 388, 904

Offset

0,1

Links

Table of n, a(n) for n=0..56.

Example

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.

Mathematica

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

Crossrefs

Cf. A067631.

Sequence in context: A308346 A192390 A272967 * A125518 A083176 A103628

Adjacent sequences: A067713 A067714 A067715 * A067717 A067718 A067719

Keyword

easy,nonn

Author

Robert G. Wilson v, Feb 05 2002

Status

approved