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A069932 Number of k, 1<=k<=n, such that phi(k) divides n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Vaclav Kotesovec, Plot of Sum_{k=1..n} a(k)/(n*log(n)) for n = 2..65537 (based on b-file)

FORMULA

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) <= A070633(n). - Antti Karttunen, Sep 10 2018

MATHEMATICA

a[n_] := Boole[ Divisible[n, EulerPhi[#]]] & /@ Range[n] // Total; Table[a[n], {n, 1, 94}] (* Jean-Fran├žois Alcover, May 23 2013 *)

PROG

(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))

(PARI) A069932(n) = sum(k=1, n, !(n%eulerphi(k))); \\ Antti Karttunen, Sep 10 2018

CROSSREFS

Cf. A000010, A070633.

Sequence in context: A005127 A140773 A133911 * A056148 A304442 A057567

Adjacent sequences:  A069929 A069930 A069931 * A069933 A069934 A069935

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 05 2002

STATUS

approved

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Last modified October 1 16:22 EDT 2020. Contains 337443 sequences. (Running on oeis4.)