

A120250


Denominator of cfenc[n] (see definition in comments).


3



1, 1, 2, 1, 3, 2, 5, 1, 3, 3, 8, 2, 13, 5, 5, 1, 21, 3, 34, 3, 8, 8, 55, 2, 4, 13, 4, 5, 89, 5, 144, 1, 13, 21, 7, 3, 233, 34, 21, 3, 377, 8, 610, 8, 7, 55, 987, 2, 7, 4, 34, 13, 1597, 4, 11, 5, 55, 89, 2584, 5, 4181, 144, 11, 1, 18, 13, 6765, 21, 89, 7, 10946, 3, 17711, 233, 7, 34
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OFFSET

1,3


COMMENTS

a[n] := denominator of cfenc[n]. cfenc[n] := number given by interpreting as a continued fraction expansion (indexed from 1) the sequence whose ith entry is one plus the exponent on the ith prime factor of n (fix cfenc[1]=1). a[2^k] = 1 a[A000040[n]] = A000045[n+1].


LINKS

Hans Havermann, Table of n, a(n) for n = 1..10000


FORMULA

a[1] = 1 a[n] = (fl = FactorInteger[n]; pq = Table[1, {i, 1, PrimePi[Last[fl][[1]]]}]; While[Length[fl] > Denominator[FromContinuedFraction[pq]])


EXAMPLE

a[2646] = Denominator[cfenc[2646]]= Denominator[cfenc[2^1 * 3^3 * 7^2]] = Denominator[FromContinuedFraction[{2; 4, 1, 3}]] = Denominator[2 + 1/(4 + 1/(1 + 1/3))] = Denominator[42/19] = 19


MATHEMATICA

Table[If[n == 1, 1, (fl = FactorInteger[n]; pq = Table[1, {i, 1, PrimePi[Last[fl][[1]]]}]; While[Length[fl] > 0, pp = First[fl]; fl = Drop[fl, 1]; pq[[PrimePi[pp[[1]]]]] = pp[[2]] + 1; ]; Denominator[FromContinuedFraction[pq]])], {n, 1, 80}]


CROSSREFS

Corresponding numerators in A120249. Numerators modulo respective denominators in A120251.
Sequence in context: A117364 A193615 A300383 * A280689 A116529 A169747
Adjacent sequences: A120247 A120248 A120249 * A120251 A120252 A120253


KEYWORD

frac,hard,nonn


AUTHOR

Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 12 2006


STATUS

approved



