Search: id:A000095
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%I A000095
%S A000095 1,2,0,0,2,0,0,0,0,4,0,0,2,0,0,0,2,0,0,0,0,0,0,0,2,4,0,0,2,0,0,0,0,4,0,
%T A000095 0,2,0,0,0,2,0,0,0,0,0,0,0,0,4,0,0,2,0,0,0,0,4,0,0,2,0,0,0,4,0,0,0,0,0,
%U A000095 0,0,2,4,0,0,0,0,0,0,0,4,0,0,4,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,2,0,0,0,0
%N A000095 Number of fixed points of GAMMA_0 (n) of type i.
%D A000095 B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, 
               p. 101.
%D A000095 G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, 
               Princeton, 1971, see p. 25, Eq. (2).
%F A000095 Multiplicative with a(2)=2, a(2^e)=0 if e>1, a(p^e)=2 if p=1 mod 4 and 
               a(p^e)=0 if p=3 mod 4. - Michael Somos, Jul 15 2004
%p A000095 A000095 := proc(n) local b,d: if irem(n,4) = 0 then RETURN(0); else b 
               := 1; for d from 2 to n do if irem(n,d) = 0 and isprime(d) then b 
               := b*(1+legendre(-1,d)); fi; od; RETURN(b); fi: end;
%t A000095 A000095[ 1 ] = 1; A000095[ n_Integer ] := If[ Mod[ n, 4 ]==0, 0, Fold[ 
               #1*(1+JacobiSymbol[ -1, #2 ])&, If[ EvenQ[ n ], 2, 1 ], Select[ First[ 
               Transpose[ FactorInteger[ n ] ] ], OddQ ] ] ]
%o A000095 (PARI) a(n)=local(t); if(n<=1|n%4==0,n==1,t=1; fordiv(n,d,if(isprime(d),
               t*=(1+kronecker(-1,d))));t) /* Michael Somos, Jul 15 2004 */
%Y A000095 Sequence in context: A107494 A079205 A107497 this_sequence A034949 A112301 
               A134013
%Y A000095 Adjacent sequences: A000092 A000093 A000094 this_sequence A000096 A000097 
               A000098
%K A000095 nonn,easy,mult
%O A000095 1,2
%A A000095 N. J. A. Sloane (njas(AT)research.att.com).

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