cp's OEIS Frontend

A118778 Total degree of the classical modular curve X_n(0). Also the degree of the classical modular polynomial.

%I A118778 #9 Oct 02 2013 16:16:06
%S A118778 1,4,6,9,10,18,14,20,20,30,22,38,26,42,40,42,34,62,38,60,56,66,46,82,
%T A118778 54,78,66,84,58,122,62,88,88,102,84,126,74,114,104,126,82,168,86,132,
%U A118778 128,138,94,172,104,166,136,156,106,198,132,170,152,174,118,254,122,186,172
%N A118778 Total degree of the classical modular curve X_n(0). Also the degree of the classical modular polynomial.
%C A118778 This is the total degree of the classical modular curve relating j(z) to j(nz), where j is the j-invariant, or elliptic modular function. If F_n(x, y) = 0 is the equation for the curve (the classical modular equation) then F_n(x, x) is the classical modular polynomial and the sequence is also the sequence of degrees for it. When n is a prime, the degree is 2n.
%D A118778 Serge Lang, ''Elliptic Functions'', Addison-Wesley, 1973.
%H A118778 T. D. Noe, <a href="/A118778/b118778.txt">Table of n, a(n) for n = 1..1000</a>
%p A118778 with(numtheory): degx := proc (n) # degree of the classical modular curve X0(n) local a, s; s := 0; for a in divisors(n) do if a^2 > n then s := s + 2*a*phi(igcd(a, n/a))/igcd(a, n/a) fi od; if issqr(n) then s := s+phi(sqrt(n)) fi; s end:
%t A118778 degx[n_] := Module[{s = 0}, Do[ If[ a^2 > n, s = s + 2*a*EulerPhi[ GCD[a, n/a]] / GCD[a, n/a]], {a, Divisors[n]}]; If[ IntegerQ[ Sqrt[n]], s = s + EulerPhi[ Sqrt[n] ] ]; s]; Table[ degx[n], {n, 1, 63}] (* _Jean-François Alcover_, Jan 29 2013, translated from Maple *)
%o A118778 (PARI) a(n)=2*sumdiv(n,d,if(d^2>n, my(g=gcd(d,n/d)); d*eulerphi(g)/g)) + if(issquare(n,&n),eulerphi(n)) \\ _Charles R Greathouse IV_, Jan 29 2013
%K A118778 nice,nonn
%O A118778 1,2
%A A118778 _Gene Ward Smith_, May 22 2006