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 A085343 #17 Jan 12 2025 17:36:48
%S A085343 0,2,1,3,1,4,1,4,3,5,1,7,1,6,5,7,1,9,1,9,6,7,1,13,3,8,5,11,1,16,1,12,
%T A085343 7,10,6,19,1,10,7,18,1,19,1,15,12,12,1,24,3,16,9,16,1,23,8,21,11,15,1,
%U A085343 33,1,14,16,20,8,26,1,19,10,25,1,35,1,19,18,23,7,30,1,31,14,18,1,39,10,19
%N A085343 Number of primes between sigma(n) and phi(n) inclusive.
%C A085343 a(p) = 1 for prime p > 2. Since phi(p) = p - 1 and sigma(p) = p + 1, the largest prime q < p - 1 must be the prime previous to p, while p itself is the largest prime less than p + 1 for p > 2. - _Michael De Vlieger_, Jan 22 2020
%H A085343 Michael De Vlieger, <a href="/A085343/b085343.txt">Table of n, a(n) for n = 1..10000</a>
%F A085343 a(n) = pi(sigma(n)) - pi(phi(n)) = A000720(A000203(n)) - A000720(A000010(n)).
%F A085343 a(n) = A070803(n) - A070804(n). - _Antti Karttunen_, Jan 22 2020
%e A085343 n=12: sigma(12)=28, phi(n)=4, Pi(28)-Pi(4)=9-2=7.
%t A085343 Array[Subtract @@ PrimePi@{DivisorSigma[1, #], EulerPhi@ #} &, 86] (* _Michael De Vlieger_, Jan 22 2020 *)
%o A085343 (PARI) a(n) = primepi(sigma(n)) - primepi(eulerphi(n)); \\ _Michel Marcus_, Aug 29 2019
%Y A085343 Cf. A000720, A000010, A000203, A070803, A070804, A085122, A085341-A085347.
%K A085343 nonn
%O A085343 1,2
%A A085343 _Labos Elemer_, Jul 10 2003