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 A182096 #21 Feb 16 2025 08:33:13 %S A182096 0,0,1,3,4,21,60,412,2912,48360,974787,56958187,2313100395, %T A182096 415655894822,24672742242739,14476157312171612,1201604193795794073, %U A182096 4552351087690759156124,597350655972004799844521,142501236416711876143177302627 %N A182096 Number of simple graphs with n unlabeled vertices with the degree of each vertex a prime number. %C A182096 A simple graph, also called a strict graph, is an unweighted, undirected graph containing no graph loops or multiple edges. Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. %H A182096 Darryn Bryant and Tom McCourt, <a href="http://wiki.smp.uq.edu.au/G-designs/index.php/Graphs_with_five_vertices">Graphs with five vertices</a>, Figure 1. %H A182096 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/SimpleGraph.html">MathWorld: Simple Graph</a> %e A182096 a(3) = 1 because there is a unique graph with 3 vertices each having prime degree, the triangle, with degree sequence (2,2,2). %e A182096 a(4) = 3 because there are 3 graphs with 4 vertices each having prime degree: the 4-cycle (2,2,2,2); the complete graph K_4 with degree sequence (3,3,3,3); and two triangle graphs sharing a common edge, with degree sequence (3,3,2,2). %e A182096 a(5) = 4 because there are 4 graphs with 5 vertices each having prime degree: the 5-cycle with degree sequence (2,2,2,2,2); a square graph sharing an edge with a triangle graph (G_13 in the linked-to illustration) with degree sequence (3,3,2,2,2); G_14 in the linked-to illustration with degree sequence (3,3,2,2,2); G_18 in the linked-to illustration with degree sequence (3,3,3,3,2). %t A182096 a[n_Integer] := Count[And @@ PrimeQ /@ GraphData[#, "Degrees"] & /@ GraphData[n], True] (* _Charles R Greathouse IV_, Apr 11 2012 *) %t A182096 show[n_Integer] := Map[Graph, GraphData[#, "EdgeRules"] & /@ %t A182096 Select[GraphData[n], And @@ PrimeQ /@ GraphData[#, "Degrees"] &]] (* _Charles R Greathouse IV_, Apr 12 2012 *) %Y A182096 Cf. A000040, A000088, A004251. %K A182096 nonn,more %O A182096 1,4 %A A182096 _Jonathan Vos Post_, Apr 11 2012 %E A182096 a(5)-a(7) from _Charles R Greathouse IV_, Apr 11 2012 %E A182096 a(8)-a(15) from _Andrew Howroyd_, Mar 08 2020 %E A182096 a(16)-a(20) from _Andrew Howroyd_, May 03 2020