A072074 Number of integers k such that phi(k) = 10^n.

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

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.

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

Cf. A000010, A014197, A014573, A110078, A072075, A072076.

Sequence in context: A280673 A363385 A280531 * A052338 A153950 A153947

Adjacent sequences: A072071 A072072 A072073 * A072075 A072076 A072077

Keyword

nonn

Author

Labos Elemer, Jun 13 2002

Extensions

More terms from Max Alekseyev, Apr 26 2010

Status

approved