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A072074
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Number of integers k such that phi(k) = 10^n.
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3
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2, 2, 4, 11, 16, 24, 43, 63, 94, 152, 224, 324, 464, 644, 897, 1271, 1790, 2521, 3501, 4814, 6535, 8779, 11739, 15585, 20625, 27166, 35588, 46363, 60065, 77424, 99337, 127020, 161930, 205847, 260929, 329782, 415533, 522173, 654548, 818278, 1020391
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OFFSET
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0,1
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COMMENTS
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a(n) is the coefficient of x^n*y^n in Product_p Sum_{u, v} x^u*y^v, where the product is taken over all primes p and the sum is taken over such u, v that 2^u*5^v = phi(p^k) for some nonnegative integer k. - Max Alekseyev, Apr 26 2010
Elaborating on above comment, primes p must be in A077497 and k must be 1 for primes other than 2 and 5. - Ray Chandler, Feb 12 2012
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LINKS
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Ray Chandler, Table of n, a(n) for n = 0..1000
Max Alekseyev, PARI scripts for various problems (see invphi.gp there).
Max A. Alekseyev, Computing the Inverses, their Power Sums, and Extrema for Euler's Totient and Other Multiplicative Functions. Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.2.
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FORMULA
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a(n) = Card{x : A000010(x)=10^n}.
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EXAMPLE
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n=3: a(3)=11 because InvPhi(1000) = {1111, 1255, 1375, 1875, 2008, 2222, 2500, 2510, 2750, 3012, 3750}.
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MAPLE
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[seq(nops(invphi(10^i)), i=1..8)];
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PROG
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(PARI) a(n) = #invphi(10^n); \\ for invphi see Alekseyev link \\ Michel Marcus, May 14 2020
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CROSSREFS
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Cf. A000010, A014197, A014573, A110078, A072075, A072076.
Sequence in context: A220786 A280673 A280531 * A052338 A153950 A153947
Adjacent sequences: A072071 A072072 A072073 * A072075 A072076 A072077
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Jun 13 2002
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EXTENSIONS
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More terms from Max Alekseyev, Apr 26 2010
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STATUS
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approved
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