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.
Array begins: 1...2...3.....4......5......6.....7.....8.....9.....10 ..2...6....12....20.....30....42.....56...72.....90 ....3...2....15......6.....35....12....63....20 ......6....30....10....210...420.....84..1260 ........5.....3.....21......2.....5....15 ...........15.....7.....42....10......3 .............105.....6.....105...30 ........
# To get first M rows of the array (s0 is A222311): g:=(i,j)->i*j/gcd(i,j)^2; M:=50; s0:=[1]: s1:=[seq(n,n=1..M)]: for i1 from 1 to M-1 do lprint(s1); s2:=[seq(g(s1[i],s1[i+1]),i=1..nops(s1)-1)]; s0:=[op(s0),s2[1]]; s1:=[seq(s2[i],i=1..nops(s2))]; od: # To produce A222310 (i.e., to read the array by antidiagonals): g:=(i,j)->i*j/gcd(i,j)^2; M:=15; b1:=Array(1..M); s0:=[1]: s1:=[seq(n,n=1..M)]: b1[1]:=s1; for i1 from 1 to M-1 do #lprint(s1); s2:=[seq(g(s1[i],s1[i+1]),i=1..nops(s1)-1)]; b1[i1+1]:=s2; s0:=[op(s0),s2[1]]; s1:=[seq(s2[i],i=1..nops(s2))]; od: #[seq(s0[i],i=1..nops(s0))]; (that gives A222311) lis:=[]: for i from 1 to M do for j from 1 to i do lis:=[op(lis),b1[i-j+1][j]]; od: od: [seq(lis[k],k=1..nops(lis))];
a = r = {1}; Do[a = Join[a, Reverse[r = FoldList[#1*#2/GCD[#1, #2]^2 &, n, r]]], {n, 2, 13}]; a (* Ivan Neretin, May 14 2015 *)
Join[r = {1}, Table[Reverse[r = FoldList[#1*#2/GCD[#1, #2]^2&, n, r]], {n, 2, 100}][[All, 1]]] (* Jean-François Alcover, Sep 04 2018, after Ivan Neretin in A222310 *)
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