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A205745
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a(n) = card { d | d*p = n, d odd, p prime }
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5
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0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 1, 2, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 1, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 1, 1, 0, 1, 1, 1, 0, 2, 1, 2
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OFFSET
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1,15
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COMMENTS
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Equivalently, a(n) is the number of prime divisors p|n such that n/p is odd. - Gus Wiseman, Jun 06 2018
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LINKS
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FORMULA
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O.g.f.: Sum_{p prime} x^p/(1 - x^(2p)). - Gus Wiseman, Jun 06 2018
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MATHEMATICA
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a[n_] := Sum[ Boole[ OddQ[d] && PrimeQ[n/d] ], {d, Divisors[n]} ]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 27 2013 *)
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PROG
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(Sage)
return sum((n//d) % 2 for d in divisors(n) if is_prime(d))
(Haskell)
a205745 n = sum $ map ((`mod` 2) . (n `div`))
[p | p <- takeWhile (<= n) a000040_list, n `mod` p == 0]
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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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