This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A061091 #51 Aug 15 2025 10:33:45
%S A061091 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 A061091 12,13,13,14,14,15,15,16,16,16,16,17,17,18,18,18,18,19,19,19,19,20,20,
%U A061091 21,21,21,21,21,21,22,22,23,23,23,23,24,24,25,25,26,26,27,27,28,28,28
%N A061091 Number of k with 1 <= k <= n relatively prime to phi(k).
%D A061091 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 115-119.
%H A061091 Seiichi Manyama, <a href="/A061091/b061091.txt">Table of n, a(n) for n = 1..10000</a>
%H A061091 Joel E. Cohen, <a href="https://arxiv.org/abs/2508.08335">Conjectures about Primes and Cyclic Numbers</a>, arXiv:2508.08335 [math.NT], 2025. See p. 2.
%H A061091 Paul 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 A061091 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 A061091 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 A061091 Paul Pollack, <a href="https://doi.org/10.1090/proc/15658">Numbers which are orders only of cyclic groups</a>, Proceedings of the American Mathematical Society, Vol. 150, No. 2 (2022), pp. 515-524; <a href="https://arxiv.org/abs/2007.09734">arXiv preprint</a>, arXiv:2007.09734 [math.NT], 2020.
%H A061091 Imre Z. Ruzsa, <a href="http://dx.doi.org/10.1006/jnth.1999.2395">Erdős and the integers</a>, J. Number Theory, Vol. 79, No. 1 (1999), 115-163.
%F A061091 Limit_{n->oo} a(n) * log(log(log(n))) / n = 1/exp(gamma).
%F A061091 a(n) = Sum_{k=1..n} gcd(k, phi(k)) = 1.
%F A061091 a(1) = 1; a(n) = a(n-1) + A297086(n). - _Iain Fox_, Dec 25 2017
%t A061091 s[n_] := Boole[CoprimeQ[n, EulerPhi[n]]]; Accumulate[Array[s, 100]] (* _Amiram Eldar_, Dec 10 2024 *)
%o A061091 (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)
%o A061091 (PARI) list(lim) = {my(s = 0); for(k = 1, lim, s += gcd(k, eulerphi(k)) == 1; print1(s, ", "));} \\ _Amiram Eldar_, Dec 10 2024
%Y A061091 Partial sums of A297086.
%Y A061091 Cf. A000010 (phi), A001620 (gamma), A003277, A073004, A080130.
%K A061091 nonn,easy
%O A061091 1,2
%A A061091 _Frank Ellermann_, May 29 2001