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Search: id:A112596
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| A112596 |
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Sequence of denominators of the continued fraction derived from the sequence of the numbers of distinct factors of a number (A001221, also called omega(n)). |
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2
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| 1, 1, 2, 3, 5, 13, 18, 31, 49, 129, 178, 485, 663, 1811, 4285, 6096, 10381, 26858, 37239, 101336, 239911, 581158, 821069, 2223296, 3044365, 8312026, 11356391, 31024808, 42381199, 158168405, 200549604, 358718009, 917985622, 2194689253, 5307364128
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The limits of the continued fraction is Cd= 0.6123687534182316423985073896748729172179677660718454489694806870..., i.e. the number associated to the sequence of number of distinct primes dividing n.
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EXAMPLE
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b[1]=1;
b[2]=d[2]*b[1] = 1*1 =1 (d[2] is the second element of A001221,
i.e. the number of distinct primes dividing 2)
b[3]=d[3]*b[2]+b[1]= 1*1+1=2
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MAPLE
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a:=proc(N) # A is numerator of the continued fraction # B is denominator of the continued fraction # d is the sequence of the number of divisors of a number (A001221), d[1] is the first element. A[1]:=d[1]; A[2]:=d[2]*A[1]+1; B[1]:=1; B[2]:=d[2]*B[1]; for n from 2 by 1 to N-1 do A[n+1]:=d[n+1]*A[n]+A[n-1]; B[n+1]:=d[n+1]*B[n]+B[n-1]; od; end:
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CROSSREFS
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Cf. A001221, A112595.
Cf.=20.
Sequence in context: A073919 A087356 A042261 this_sequence A041385 A108282 A042047
Adjacent sequences: A112593 A112594 A112595 this_sequence A112597 A112598 A112599
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KEYWORD
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frac,nonn
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AUTHOR
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Giorgio Balzarotti and Paolo P. Lava (greenblue(AT)tiscali.it), Dec 19 2005
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