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A182043 Table, by rows, of T(k,n) the number of simple graphs on v = prime(n) vertices and with e = prime(k) edges.

%I A182043 #26 Feb 16 2025 08:33:13
%S A182043 1,1,2,4,6,4,2,5,21,65,148,97,10,2,2,5,26,172,10250,75415,2295898,
%T A182043 8640134,53037356,99187806,70065437,4609179,192788,28259,467,2,2,5,26,
%U A182043 176,14140,154658,17422984,152339952,6461056816,359954668522,899632282299,4093273437761,4093273437761
%N A182043 Table, by rows, of T(k,n) the number of simple graphs on v = prime(n) vertices and with e = prime(k) edges.
%H A182043 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SimpleGraph.html">Simple Graph</a>.
%e A182043 T(3,4) = 4 because there are 4 simple graphs with prime(3) = 5 vertices and prime(4) = 7 edges.
%e A182043 The table begins:
%e A182043       +---+---+---+---+
%e A182043       |e=2|e=3|e=5|e=7|
%e A182043   +---+---+---+---+---+
%e A182043   |v=3| 1 | 1 |   |   |
%e A182043   +---+---+---+---+---+
%e A182043   |v=5| 2 | 4 | 6 | 4 |
%e A182043   +---+---+---+---+---+
%p A182043 read("transforms3") :
%p A182043 L := BFILETOLIST("b008406.txt") ;
%p A182043 A008406 := proc(n,k)
%p A182043     global L ;
%p A182043     local f,r ;
%p A182043     f := 1 ;
%p A182043     r := 1 ;
%p A182043     while r < n do
%p A182043         f := f+r*(r-1)/2+1 ;
%p A182043         r := r+1 ;
%p A182043     end do:
%p A182043     op(f+k,L) ;
%p A182043 end proc:
%p A182043 for n from 1 do
%p A182043     v := ithprime(n) ;
%p A182043     for k from 1 do
%p A182043         e := ithprime(k) ;
%p A182043         if e > v*(v-1)/2 then
%p A182043             break;
%p A182043         else
%p A182043             printf("%d,",A008406(v,e)) ;
%p A182043         end if;
%p A182043     end do:
%p A182043 end do: # _R. J. Mathar_, Oct 20 2013
%Y A182043 Cf. A008406.
%K A182043 nonn,tabf
%O A182043 2,3
%A A182043 _Jonathan Vos Post_, Apr 07 2012
%E A182043 Terms from row 4 on by _R. J. Mathar_, Oct 20 2013