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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) = 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 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

Card{x : A000010(x)=10^n} = nops(invphi(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)];

CROSSREFS

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

Sequence in context: A280673 A067920 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

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Last modified September 26 10:59 EDT 2017. Contains 292518 sequences.