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 A082767 #25 Jun 24 2022 22:40:57
%S A082767 1,3,5,7,9,12,14,16,18,21,23,26,28,31,34,36,38,41,43,46,49,52,54,57,
%T A082767 59,62,64,67,69,73,75,77,80,83,86,89,91,94,97,100,102,106,108,111,114,
%U A082767 117,119,122,124,127,130,133,135,138,141,144,147,150,152,156,158,161,164,166,169,173
%N A082767 Number of edges in the prime graph.
%C A082767 The prime graph is defined to be the graph formed by writing the integers 0 to n in a straight line as vertices and then connecting i and j (i > j) iff i-j=1 or i=j+p, where p is a prime factor of i. It can be visualized as the Sieve of Eratosthenes, with each integer connected to its neighbors and the striking out process as a wave forming the remaining edges.
%H A082767 Vincenzo Librandi, <a href="/A082767/b082767.txt">Table of n, a(n) for n = 1..2000</a>
%F A082767 a(n) = a(n-1) + 1 + omega(n) if n > 1, with a(1) = 1, where omega(n) is the number of distinct prime factors of n.
%F A082767 a(n) = Sum_{p is 1 or a prime, p <= n} floor(n/p); e.g., a(12) = floor(12/1) + floor(12/2) + floor(12/30) + floor(12/5) + floor(12/7) + floor(12/11) = 12 + 6 + 4 + 2 + 1 + 1 = 26. - _Amarnath Murthy_, Jul 06 2005
%e A082767 a(1) = 1.
%e A082767 a(2) = a(1) + 1 + omega(2) = 1 + 1 + 1 = 3.
%e A082767 a(6) = a(5) + 1 + omega(6) = 9 + 1 + 2 = 12.
%t A082767 Accumulate[PrimeNu[Range[120]] + 1] (* _Vincenzo Librandi_, Jun 10 2017 *)
%o A082767 (PARI) a=1; c=2; while (c<50,print1(a","); a=a+1+omega(c); c++)
%o A082767 (Magma) I:=[1]; [n le 1 select I[n] else Self(n-1)+1+#PrimeDivisors(n): n in [1..70]]; // _Vincenzo Librandi_, Jun 10 2017
%Y A082767 Partial sums of A083399.
%K A082767 nonn
%O A082767 1,2
%A A082767 _Jon Perry_, May 24 2003
%E A082767 Corrected by _T. D. Noe_, Oct 25 2006