A317926 - OEIS

%I #9 Dec 12 2022 01:34:07

%S 1,2,1,8,1,2,1,16,2,1,1,8,1,2,1,128,1,4,1,4,1,2,1,16,1,1,2,8,1,1,1,

%T 256,1,1,1,16,1,2,1,8,1,2,1,8,1,2,1,128,2,1,1,4,1,4,1,16,1,1,1,4,1,2,

%U 2,1024,1,2,1,1,1,1,1,32,1,1,1,8,1,1,1,64,8,1,1,8,1,2,1,16,1,2,1,8,1,2,1,256,1,4,2,1,1,1,1,8,1

%N Denominators of rational valued sequence whose Dirichlet convolution with itself yields Euler's phi (A000010).

%H Antti Karttunen, <a href="/A317926/b317926.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A000010(n) - Sum_{d|n, d>1, d<n} f(d) * f(n/d)) for n > 1.

%t f[1] = 1; f[n_] := f[n] = (EulerPhi[n] - DivisorSum[n, f[#]*f[n/#] &, 1 < # < n &])/2; Denominator @ Array[f, 100] (* _Amiram Eldar_, Dec 12 2022 *)

%o (PARI)

%o A317925perA317926(n) = if(1==n,n,(eulerphi(n)-sumdiv(n,d,if((d>1)&&(d<n),A317925perA317926(d)*A317925perA317926(n/d),0)))/2);

%o A317926(n) = denominator(A317925perA317926(n));

%Y Cf. A000010, A317925 (numerators).

%Y Cf. also A046644, A317832.

%K nonn,frac

%O 1,2

%A _Antti Karttunen_, Aug 11 2018