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A055654
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Difference between n and the result of "Phi-summation" over unitary divisors of n.
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3
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0, 0, 0, 1, 0, 0, 0, 3, 2, 0, 0, 3, 0, 0, 0, 7, 0, 4, 0, 5, 0, 0, 0, 9, 4, 0, 8, 7, 0, 0, 0, 15, 0, 0, 0, 15, 0, 0, 0, 15, 0, 0, 0, 11, 10, 0, 0, 21, 6, 8, 0, 13, 0, 16, 0, 21, 0, 0, 0, 15, 0, 0, 14, 31, 0, 0, 0, 17, 0, 0, 0, 37, 0, 0, 12, 19, 0, 0, 0, 35, 26, 0, 0, 21, 0, 0, 0, 33, 0, 20, 0, 23
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OFFSET
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1,8
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COMMENTS
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Squarefree numbers are roots of a(n)=0 equation, while Min n for which a(n)=k is k^2. See also A000188, A008833.
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LINKS
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FORMULA
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a(n) = n - Sum_{u|n, gcd(u,n/u) = 1} phi(u), i.e. when u is a unitary divisor of n.
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MATHEMATICA
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Table[n - DivisorSum[n, EulerPhi[#] &, CoprimeQ[#, n/#] &], {n, 92}] (* Michael De Vlieger, Oct 26 2017 *)
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PROG
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(Haskell)
a055654 n = a055654_list !! (n-1)
a055654_list = zipWith (-) [1..] a055653_list
(PARI) a(n) = n - sumdiv(n, d, if (gcd(d, n/d)==1, eulerphi(d))); \\ Michel Marcus, Oct 27 2017
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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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