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A061091 Number of k with 1 <= k <= n relatively prime to phi(k). 2

%I

%S 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,

%T 12,13,13,14,14,15,15,16,16,16,16,17,17,18,18,18,18,19,19,19,19,20,20,

%U 21,21,21,21,21,21,22,22,23,23,23,23,24,24,25,25,26,26,27,27,28,28,28

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

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

%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 115-119.

%H Seiichi Manyama, <a href="/A061091/b061091.txt">Table of n, a(n) for n = 1..10000</a>

%H P. Erdős, <a href="https://www.renyi.hu/~p_erdos/1948-11.pdf">Some asymptotic formulas in number theory</a>, J. Indian Math. Soc. 12 (1948) 75-78.

%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/totient/totient.html">Euler Totient Function Asymptotic Constants</a> [Broken link]

%H Steven R. Finch, <a href="http://web.archive.org/web/20010603070928/http://www.mathsoft.com/asolve/constant/totient/totient.html">Euler Totient Function Asymptotic Constants</a> [From the Wayback machine]

%H Z. Ruzsa, <a href="http://dx.doi.org/10.1006/jnth.1999.2395">Erdős and the integers</a>, J. Number Theory 79 (1999) 115-163.

%F a(n) = sum of GCD( k, phi(k)) = 1 for 0 < k <= n.

%F a(1) = 1, a(n) = a(n-1) + A297086(n). - _Iain Fox_, Dec 25 2017

%o (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)

%Y Gamma function: A001620, phi function: A000010.

%K nonn,easy

%O 1,2

%A _Frank Ellermann_, May 29 2001

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)