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%I #33 May 14 2020 07:49:33
%S 2,2,4,11,16,24,43,63,94,152,224,324,464,644,897,1271,1790,2521,3501,
%T 4814,6535,8779,11739,15585,20625,27166,35588,46363,60065,77424,99337,
%U 127020,161930,205847,260929,329782,415533,522173,654548,818278,1020391
%N Number of integers k such that phi(k) = 10^n.
%C 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
%C 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
%H Ray Chandler, <a href="/A072074/b072074.txt">Table of n, a(n) for n = 0..1000</a>
%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI scripts for various problems</a> (see invphi.gp there).
%H Max A. Alekseyev, <a href="https://www.emis.de/journals/JIS/VOL19/Alekseyev/alek5.html">Computing the Inverses, their Power Sums, and Extrema for Euler's Totient and Other Multiplicative Functions</a>. Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.2.
%F a(n) = Card{x : A000010(x)=10^n}.
%e n=3: a(3)=11 because InvPhi(1000) = {1111, 1255, 1375, 1875, 2008, 2222, 2500, 2510, 2750, 3012, 3750}.
%p [seq(nops(invphi(10^i)),i=1..8)];
%o (PARI) a(n) = #invphi(10^n); \\ for invphi see Alekseyev link \\ _Michel Marcus_, May 14 2020
%Y Cf. A000010, A014197, A014573, A110078, A072075, A072076.
%K nonn
%O 0,1
%A _Labos Elemer_, Jun 13 2002
%E More terms from _Max Alekseyev_, Apr 26 2010
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