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A065338
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a(1) = 1, a(p) = p mod 4 for p prime and a(u * v) = a(u) * a(v) for u, v > 0.
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20
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1, 2, 3, 4, 1, 6, 3, 8, 9, 2, 3, 12, 1, 6, 3, 16, 1, 18, 3, 4, 9, 6, 3, 24, 1, 2, 27, 12, 1, 6, 3, 32, 9, 2, 3, 36, 1, 6, 3, 8, 1, 18, 3, 12, 9, 6, 3, 48, 9, 2, 3, 4, 1, 54, 3, 24, 9, 2, 3, 12, 1, 6, 27, 64, 1, 18, 3, 4, 9, 6, 3, 72, 1, 2, 3, 12, 9, 6, 3, 16, 81, 2, 3, 36, 1, 6, 3, 24, 1, 18, 3
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) <= n.
a(a(n)) = a(n).
a(x) = x iff x = 2^i * 3^j for i, j >= 0.
Dirichlet g.f.: (1/(1-2^(-s+1))) * Product_{prime p=4k+1} (1/(1-p^(-s))) * Product_{prime p=4k+3} 1/(1-3*p^(-s)). - Ralf Stephan, Mar 28 2015
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EXAMPLE
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a(120) = a(2*2*2*3*5) = a(2)*a(2)*a(2)*a(3)*a(5) = 2*2*2*3*1 = 24.
a(150) = a(2*3*5*5) = a(2)*a(3)*a(5)*a(5) = 2*3*1*1 = 6.
a(210) = a(2*3*5*7) = a(2)*a(3)*a(5)*a(7) = 2*3*1*3 = 18.
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = Mod[p = FactorInteger[n][[1, 1]], 4]*a[n/p]; Table[ a[n], {n, 1, 100} ] (* Jean-François Alcover, Jan 20 2012 *)
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PROG
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(Haskell)
a065338 1 = 1
a065338 n = (spf `mod` 4) * a065338 (n `div` spf) where spf = a020639 n
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CROSSREFS
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KEYWORD
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mult,nice,nonn
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AUTHOR
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STATUS
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approved
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