

A308945


Number of totient numbers, phi(k), k <= 10^n, whose initial digit is 1.


0



2, 20, 213, 2152, 21594, 216009, 2159776, 21595522, 215951111, 2159507603, 21595061256, 215950604593
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OFFSET

1,1


COMMENTS

The probability that a totient number starts with an initial 1 does not obey Benford's law however it does appear to tend to a constant value. In a sample of 10^9 totient numbers the distribution of initial digits 1  9 is approx. 21.595%, 20.774%, 16.457%, 12.682%, 7.904%, 6.633%, 5.505%, 4.634%, 3.816%.


LINKS



EXAMPLE

a(1)=2 as the first 10 totient numbers are {1, 1, 2, 2, 4, 2, 6, 4, 6, 4} and the occurrence of numbers with an initial 1 is 2.


MATHEMATICA

lst1={}; Do[lst=Table[0, {n, 1, 9}]; Do[++lst[[First@IntegerDigits@EulerPhi[n]]], {n, 1, 10^m}]; AppendTo[lst1, lst[[1]]], {m, 1, 7}]; lst1


PROG

(PARI) a(n) = {k=0; for(j=1, 10^n, if(digits(eulerphi(j))[1]==1, k++)); k} \\ Jinyuan Wang, Jul 04 2019


CROSSREFS



KEYWORD

nonn,base,more


AUTHOR



EXTENSIONS



STATUS

approved



