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A000095
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Number of fixed points of GAMMA_0 (n) of type i.
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1
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 101.
G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton, 1971, see p. 25, Eq. (2).
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FORMULA
| 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
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MAPLE
| 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;
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MATHEMATICA
| 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 ] ] ]
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PROG
| (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 */
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CROSSREFS
| Sequence in context: A107494 A079205 A107497 * A034949 A112301 A134013
Adjacent sequences: A000092 A000093 A000094 * A000096 A000097 A000098
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KEYWORD
| nonn,easy,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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