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A069932
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Number of k, 1<=k<=n, such that phi(k) divides n.
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6
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1, 2, 2, 4, 2, 5, 2, 7, 2, 5, 2, 11, 2, 5, 2, 11, 2, 9, 2, 10, 2, 5, 2, 19, 2, 5, 2, 9, 2, 11, 2, 16, 2, 5, 2, 20, 2, 5, 2, 18, 2, 9, 2, 10, 2, 5, 2, 32, 2, 7, 2, 9, 2, 13, 2, 15, 2, 5, 2, 26, 2, 5, 2, 22, 2, 11, 2, 9, 2, 7, 2, 38, 2, 5, 2, 9, 2, 9, 2, 30, 2, 5, 2, 23, 2, 5, 2, 17, 2, 17, 2, 10, 2, 5
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OFFSET
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1,2
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COMMENTS
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Unlike A070633, this sequence does not give the number of all integers of the form phi(k) dividing n (for some n and some m > n, phi(m) divides n).
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LINKS
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FORMULA
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Asymptotically (still conjectured): sum(k=1, n, a(k)) = C*n*log(n) + o(n*log(n)) with C=1.5...
G.f.: Sum_{k>=1} 1/(1-x^phi(k)).
a(n) = Sum_{k=1..n} (1 - ceiling(n/phi(k)) + floor(n/phi(k))). - Wesley Ivan Hurt, Apr 21 2023
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MATHEMATICA
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a[n_] := Boole[ Divisible[n, EulerPhi[#]]] & /@ Range[n] // Total; Table[a[n], {n, 1, 94}] (* Jean-François Alcover, May 23 2013 *)
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PROG
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(PARI) for(n=1, 150, print1(sum(i=1, n, if(n%eulerphi(i), 0, 1)), ", "))
(PARI) a(n)=if(n<1, 0, polcoeff(sum(k=1, n, 1/(1-x^eulerphi(k)), x*O(x^n)), n))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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