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a(0)=1; a(n) = Sum_{1<=k<=n, gcd(k,n)=1} a(floor(k/2)), where the sum is over those positive integers which are <= n and are coprime to n.
0

%I #12 Aug 02 2019 23:22:37

%S 1,1,1,2,2,4,2,7,5,8,6,17,8,23,11,20,20,44,15,57,25,40,35,94,40,101,

%T 62,114,79,184,50,215,118,155,133,247,123,378,189,311,194,532,117,597,

%U 295,373,337,801,297,825,393,741,530,1239,399,1088,673,1042,833,1871,530

%N a(0)=1; a(n) = Sum_{1<=k<=n, gcd(k,n)=1} a(floor(k/2)), where the sum is over those positive integers which are <= n and are coprime to n.

%e The positive integers which are <= 12 and are coprime to 12 are 1,5,7,11. Dividing each of these by 2 and rounding down, we get 0,2,3,5. So a(12) = a(0) + a(2) + a(3) + a(5) = 1+1+2+4 = 8.

%t a = {1}; For[n = 1, n < 70, n++, s = 0; b = Select[Range[n], GCD[n, # ] == 1 &]; For[j = 1, j < Length[b] + 1, j++, s = s + a[[Floor[b[[j]]/2] + 1]]]; AppendTo[a, s]]; a (* _Stefan Steinerberger_, Nov 20 2007 *)

%K nonn

%O 0,4

%A _Leroy Quet_, Nov 17 2007

%E More terms from _Stefan Steinerberger_, Nov 20 2007