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 A241194 #42 Aug 11 2025 04:45:12
%S A241194 1,1,1,1,2,1,1,1,5,3,4,1,2,2,11,6,14,4,10,12,1,4,20,5,1,2,16,26,1,3,2,
%T A241194 24,8,22,18,4,4,1,41,21,44,4,36,1,3,10,8,12,56,6,14,48,4,2,1,65,33,4,
%U A241194 22,12,46,36,16,12,4,39,8,2,86,28,5,89,20,10,2,95
%N A241194 Numerator of phi(p-1)/(p-1), where phi is Euler's totient function and p = prime(n).
%C A241194 The denominators are in A241195. The new minima of phi(p-1)/(p-1) occur at primes listed in A241196. The numerator and denominator of those terms are in A241197 and A241198.
%C A241194 For primes p>2, the fraction phi(p - 1)/(p - 1) has the maximum value = 1/2 if and only if p is in A019434. - _Geoffrey Critzer_, Dec 30 2014
%D A241194 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 117.
%H A241194 T. D. Noe, <a href="/A241194/b241194.txt">Table of n, a(n) for n = 1..10000</a>
%H A241194 P. Erdős, <a href="http://www.renyi.hu/~p_erdos/1938-09.pdf">On the density of some sequences of numbers, III.</a>, J. London Math. Soc. 13 (1938), pp. 119-127.
%H A241194 Imre Kátai, <a href="http://archive.numdam.org/article/CM_1968__19_4_278_0.pdf">On distribution of arithmetical functions on the set prime plus one</a>, Compositio Math. 19 (1968), pp. 278-289.
%H A241194 I. J. Schoenberg, <a href="https://gdz.sub.uni-goettingen.de/id/PPN266833020_0028">Über die asymptotische Verteilung reeller Zahlen mod 1</a>, Mathematische Zeitschrift 28:1 (1928), pp. 171-199.
%F A241194 From _Amiram Eldar_, Jul 31 2020: (Start)
%F A241194 Asymptotic mean: lim_{m->oo} (1/m) * Sum_{n=1..m} a(n)/A241195(n) = 0.373955... (Artin's constant, A005596).
%F A241194 Asymptotic mean of inverse ratio: lim_{m->oo} (1/m) * Sum_{n=1..m} A241195(n)/a(n) = 2.826419... (Murata's constant, A065485). (End)
%F A241194 a(n) = A076512(A006093(n)). - _Ridouane Oudra_, Mar 24 2025
%p A241194 seq(numer(numtheory:-phi(ithprime(i)-1)/(ithprime(i)-1)), i=1..100); # _Robert Israel_, Jan 11 2015
%t A241194 Numerator[Table[EulerPhi[p - 1]/(p - 1), {p, Prime[Range[100]]}]]
%o A241194 (PARI) lista(nn) = forprime(p=2, nn, print1(numerator(eulerphi(p-1)/(p-1)), ", ")); \\ _Michel Marcus_, Jan 03 2015
%o A241194 (Magma) [Numerator(EulerPhi(NthPrime(n)-1)/(NthPrime(n)-1)): n in [1..80]]; // _Vincenzo Librandi_, Apr 06 2015
%Y A241194 Cf. A000010, A005596, A008330 (phi(prime(n)-1)), A065485, A241195, A241196, A241197, A241198.
%Y A241194 Cf. A076512, A006093.
%K A241194 nonn,frac
%O A241194 1,5
%A A241194 _T. D. Noe_, Apr 17 2014