A127614 a(n) = numerator of the continued fraction which has the positive integers which are <= n and are coprime to n as its terms.

1, 1, 3, 4, 43, 6, 1393, 151, 3980, 265, 7489051, 479, 1004933203, 28065, 1567857, 3025576, 44811373131073, 107069, 13807296146243251, 12541924, 85867066404, 1867630045, 2448516766522879398193, 47040432, 85536466996746340043

Offset

1,3

Comments

The positive integers coprime to n and <= n can be written either from largest to smallest or from smallest to largest and the numerator of the continued fraction would remain unchanged.

Links

Table of n, a(n) for n=1..25.

Example

The positive integers coprime to 8 and <= 8 are 1,3,5,7. So a(8) is the numerator of 1 +1/(3 +1/(5 +1/7)) = 151/115. a(8) is also the numerator of 7 +1/(5 +1/(3 +1/1)) = 151/21.

Mathematica

f[n_] := Select[Range[n], GCD[ #, n] == 1 &]; g[n_] := Numerator[FromContinuedFraction[f[n]]]; Table[g[n], {n, 26}] (* Ray Chandler, Jan 22 2007 *)

Crossrefs

Cf. A127615, A127616.

Sequence in context: A348225 A172144 A032837 * A041055 A246626 A032838

Adjacent sequences: A127611 A127612 A127613 * A127615 A127616 A127617

Keyword

frac,nonn

Author

Leroy Quet, Jan 19 2007

Extensions

Extended by Ray Chandler, Jan 22 2007

Status

approved