A029936 Number of cusps of Gamma_1(n)\P_1(Q).

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, 30, 30, 28, 32, 30, 32, 40, 32, 48, 40, 36, 36, 48, 48, 40, 48, 42, 50, 64, 44, 46, 56, 60, 56, 64, 60, 52, 60, 80, 72, 72, 56

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Programs

Mathematica

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 *)

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

Formula

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

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