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A200726
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Define a map f from primes to integers mod 4 by f(p) = 0,1,3,2,1 according as p == 1,2,3,4,0 mod 5; a(n) = Sum_{all primes p} v_p(n)*f(p), where v_p(n) is the exponent of the highest power of p dividing n.
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1
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0, 1, 3, 2, 1, 0, 1, 3, 2, 2, 0, 1, 3, 2, 0, 0, 1, 3, 2, 3, 0, 1, 3, 2, 2, 0, 1, 3, 2, 1, 0, 1, 3, 2, 2, 0, 1, 3, 2, 0, 0, 1, 3, 2, 3, 0, 1, 3, 2, 3, 0, 1, 3, 2, 1, 0, 1, 3, 2, 2, 0, 1, 3, 2, 0, 0, 1, 3, 2, 3, 0, 1, 3, 2, 1, 0, 1, 3, 2, 1, 0, 1, 3, 2, 2, 0, 1, 3, 2
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OFFSET
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1,3
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COMMENTS
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All calculations are done mod 4.
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LINKS
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EXAMPLE
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n=4: v_2(4)=2, v_p(4)=0 for p>2, so a(4)=2*f(2)=2*1=2.
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MAPLE
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with(padic) ;
A200726f := proc(p)
op(1+(p mod 5), [1, 0, 1, 3, 2]) ;
end proc:
local a, e;
a := 0 ;
for e in ifactors(n)[2] do
p := op(1, e) ;
a := a+ ordp(n, p)*A200726f(p) ;
end do:
return (a mod 4 );
end proc:
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MATHEMATICA
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f[p_] := {1, 0, 1, 3, 2}[[Mod[p, 5] + 1]];
a[1] = 0; a[n_] := Sum[IntegerExponent[n, p]*f[p], {p, FactorInteger[n][[ All, 1]]}] // Mod[#, 4]&;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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