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 A128913 #35 Jul 14 2025 08:03:06
%S A128913 0,2,6,8,15,18,28,32,36,40,55,60,78,84,90,96,119,126,152,160,168,176,
%T A128913 207,216,225,234,243,252,290,300,341,352,363,374,385,396,444,456,468,
%U A128913 480,533,546,602,616,630,644,705,720,735,750,765,780,848,864,880,896
%N A128913 a(n) = n*pi(n).
%C A128913 Pi(n) = number of primes <= n (see A000720).
%C A128913 Conjecture: For each n there is at least one prime p such that 2*a(n) < p < 2*a(n+1). From the conjecture follows that the prime gaps g(n) = prime(n+1) - prime(n) = O(sqrt(prime(n)/log(prime(n)))). - _Thomas Ordowski_, Aug 12 2012
%C A128913 Number of primes that are obtained when listing all reduced fractions i/j with 1<=i,j<=n. - _Michel Marcus_, Sep 09 2015
%F A128913 a(n) = n*A000720(n).
%F A128913 a(n) ~ n^2/log n. - _Thomas Ordowski_, Aug 12 2012
%F A128913 G.f.: x*f'(x), where f(x) = Sum_{k>=1} x^prime(k)/(1 - x). - _Ilya Gutkovskiy_, Apr 10 2017
%e A128913 a(7) = 28 because there are four primes less than or equal to 7 (namely 2, 3, 5, 7) and 7 * 4 = 28.
%t A128913 Table[n PrimePi[n], {n, 60}] (* _Alonso del Arte_, Aug 14 2012 *)
%o A128913 (PARI) a(n) = n*primepi(n);
%Y A128913 Cf. A000720, A128930.
%K A128913 easy,nonn
%O A128913 1,2
%A A128913 _Cino Hilliard_, Apr 23 2007