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Search: id:A112595
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| A112595 |
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Sequence of numerators of the continued fraction derived from the sequence of the number of distinct factors of a number (A001221, also called omega (n)). |
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+0
2
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| 0, 1, 1, 2, 3, 8, 11, 19, 30, 79, 109, 297, 406, 1109, 2624, 3733, 6357, 16447, 22804, 62055, 146914, 355883, 502797, 1361477, 1864274, 5090025, 6954299, 18998623, 25952922, 96857389, 122810311, 219667700, 562145711, 1343959122, 3250063955
(list; graph; listen)
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OFFSET
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1,4
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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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a[1]=d[1]=0 (d[1] is the first element of A001221,
i.e. the number of distinct primes dividing 1 )
a[2]=d[2]*a[1]+1=0*1+1=1;
a[3]=d[3]*a[2]+a[1]=1*1+0=1
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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, A112596.
Sequence in context: A119116 A138756 A091076 this_sequence A041075 A041893 A007676
Adjacent sequences: A112592 A112593 A112594 this_sequence A112596 A112597 A112598
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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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