login
a(n) = denominator of the continued fraction which has the positive integers which are <= n and are coprime to n as its terms. The terms are written in order from 1 for the integer part, to n-1 for the final term of the continued fraction.
2

%I #9 Oct 10 2019 11:32:28

%S 1,1,2,3,30,5,972,115,2751,201,5225670,401,701216922,21376,1084178,

%T 2304261,31268240559432,89634,9634381345852650,9512947,59351535853,

%U 1422376141,1708512949279640961732,39380419,59683863841431305060

%N a(n) = denominator of the continued fraction which has the positive integers which are <= n and are coprime to n as its terms. The terms are written in order from 1 for the integer part, to n-1 for the final term of the continued fraction.

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

%t f[n_] := Select[Range[n], GCD[ #, n] == 1 &];g[n_] := Denominator[FromContinuedFraction[f[n]]];Table[g[n], {n, 26}] (* _Ray Chandler_, Jan 22 2007 *)

%Y Cf. A127614, A127616.

%K frac,nonn

%O 1,3

%A _Leroy Quet_, Jan 19 2007

%E Extended by _Ray Chandler_, Jan 22 2007