A029936 - OEIS

%I #17 Dec 15 2017 07:26:59

%S 1,2,2,3,4,4,6,6,8,8,10,10,12,12,16,14,16,16,18,20,24,20,22,24,28,24,

%T 30,30,28,32,30,32,40,32,48,40,36,36,48,48,40,48,42,50,64,44,46,56,60,

%U 56,64,60,52,60,80,72,72,56

%N Number of cusps of Gamma_1(n)\P_1(Q).

%D F. Hirzebruch et al., Manifolds and Modular Forms, Vieweg, 2nd ed. 1994, p. 158.

%H G. C. Greubel, <a href="/A029936/b029936.txt">Table of n, a(n) for n = 1..10000</a>

%F Except for n=1, 2, 4, this is A029935(n)/2.

%F a(n) = (1/2)*Sum_{d divides n} phi(d)*phi(n/d), with a(1)=1, a(2)=2, a(3)=2, a(4)=3, and phi(n) = A000010(n). - _G. C. Greubel_, Dec 13 2017

%t a[1] = 1; a[2] = 2; a[4] = 3; a[n_] := DivisorSum[n, EulerPhi[#]* EulerPhi[n/#]&]/2; Array[a, 60] (* _Jean-François Alcover_, Oct 03 2016 *)

%o (PARI) for(n=1,30, print1(if(n==1, 1, if(n==2, 2, if(n==3, 2, if(n==4, 3, sumdiv(n, d, eulerphi(d)*eulerphi(n/d))/2)))), ", ")) \\ _G. C. Greubel_, Dec 13 2017

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_