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%I #11 Feb 18 2024 04:32:54
%S 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,
%T 144,1,13,21,7,3,233,34,21,3,377,8,610,8,7,55,987,2,7,4,34,13,1597,4,
%U 11,5,55,89,2584,5,4181,144,11,1,18,13,6765,21,89,7,10946,3,17711,233,7,34
%N Denominator of cfenc(n) (see definition in comments).
%C a(n) := denominator of cfenc(n). cfenc(n) := number given by interpreting as a continued fraction expansion (indexed from 1) the sequence whose i-th entry is one plus the exponent on the i-th prime factor of n (fix cfenc(1)=1). a(2^k) = 1; a(prime(n)) = Fibonacci(n+1).
%H Hans Havermann, <a href="/A120250/b120250.txt">Table of n, a(n) for n = 1..10000</a>
%F a(1) = 1; a(n) = (fl = FactorInteger[n]; pq = Table[1, {i, 1, PrimePi[Last[fl][[1]]]}]; While[Length[fl] > Denominator[FromContinuedFraction[pq]])
%e 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.
%t 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}]
%Y Corresponding numerators in A120249. Numerators modulo respective denominators in A120251.
%K frac,nonn,uned
%O 1,3
%A Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 12 2006
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