

A061091


Number of k with 1 <= k <= n relatively prime to phi(k).


2



1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 28
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OFFSET

1,2


COMMENTS

lim_{n>oo} a(n) * log(log(log( n ))) / n = 1 / exp( gamma ).


REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 115119.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000
P. Erdős, Some asymptotic formulas in number theory, J. Indian Math. Soc. 12 (1948) 7578.
S. R. Finch, Euler Totient Function Asymptotic Constants
Z. Ruzsa, Erdős and the integers, J. Number Theory 79 (1999) 115163.


FORMULA

a(n) = sum of GCD( k, phi(k)) = 1 for 0 < k <= n.
a(1) = 1, a(n) = a(n1) + A297086(n).  Iain Fox, Dec 25 2017


PROG

(PARI) a(n) = sum(k=1, n, gcd(k, eulerphi(k)) == 1) \\ Charles R Greathouse IV, Jan 29 2013 (corrected by Iain Fox, Dec 25 2017)


CROSSREFS

Gamma function: A001620, phi function: A000010.
Sequence in context: A185195 A192512 A036234 * A196241 A086592 A279783
Adjacent sequences: A061088 A061089 A061090 * A061092 A061093 A061094


KEYWORD

nonn,easy


AUTHOR

Frank Ellermann, May 29 2001


STATUS

approved



