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A072074
Number of integers k such that phi(k) = 10^n.
3
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
OFFSET
0,1
COMMENTS
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
LINKS
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.
FORMULA
a(n) = Card{x : A000010(x)=10^n}.
EXAMPLE
n=3: a(3)=11 because InvPhi(1000) = {1111, 1255, 1375, 1875, 2008, 2222, 2500, 2510, 2750, 3012, 3750}.
MAPLE
[seq(nops(invphi(10^i)), i=1..8)];
PROG
(PARI) a(n) = #invphi(10^n); \\ for invphi see Alekseyev link \\ Michel Marcus, May 14 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 13 2002
EXTENSIONS
More terms from Max Alekseyev, Apr 26 2010
STATUS
approved