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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A280673 A363385 A280531 * A052338 A153950 A153947
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 13 2002
EXTENSIONS
More terms from Max Alekseyev, Apr 26 2010
STATUS
approved

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Last modified February 29 07:23 EST 2024. Contains 370414 sequences. (Running on oeis4.)