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%I #25 Feb 25 2020 02:14:11
%S 1,1,2,4,6,4,2,5,21,65,148,97,10,2,2,5,26,172,10250,75415,2295898,
%T 8640134,53037356,99187806,70065437,4609179,192788,28259,467,2,2,5,26,
%U 176,14140,154658,17422984,152339952,6461056816,359954668522,899632282299,4093273437761,4093273437761
%N Table, by rows, of T(k,n) the number of simple graphs on v = prime(n) vertices and with e = prime(k) edges.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SimpleGraph.html">Simple Graph</a>.
%e T(3,4) = 4 because there are 4 simple graphs with prime(3) = 5 vertices and prime(4) = 7 edges.
%e The table begins:
%e +---+---+---+---+
%e |e=2|e=3|e=5|e=7|
%e +---+---+---+---+---+
%e |v=3| 1 | 1 | | |
%e +---+---+---+---+---+
%e |v=5| 2 | 4 | 6 | 4 |
%e +---+---+---+---+---+
%p read("transforms3") :
%p L := BFILETOLIST("b008406.txt") ;
%p A008406 := proc(n,k)
%p global L ;
%p local f,r ;
%p f := 1 ;
%p r := 1 ;
%p while r < n do
%p f := f+r*(r-1)/2+1 ;
%p r := r+1 ;
%p end do:
%p op(f+k,L) ;
%p end proc:
%p for n from 1 do
%p v := ithprime(n) ;
%p for k from 1 do
%p e := ithprime(k) ;
%p if e > v*(v-1)/2 then
%p break;
%p else
%p printf("%d,",A008406(v,e)) ;
%p end if;
%p end do:
%p end do: # _R. J. Mathar_, Oct 20 2013
%Y Cf. A008406.
%K nonn,tabf
%O 2,3
%A _Jonathan Vos Post_, Apr 07 2012
%E Terms from row 4 on by _R. J. Mathar_, Oct 20 2013
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