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 A356300 #7 Aug 03 2022 15:27:49
%S A356300 1,1,1,1,2,1,1,2,2,1,1,2,3,2,1,1,2,2,2,2,1,1,2,3,4,3,2,1,1,2,2,2,2,2,
%T A356300 2,1,1,2,3,4,5,4,3,2,1,1,2,2,2,2,2,2,2,2,1,1,2,3,4,5,6,5,4,3,2,1,1,2,
%U A356300 2,2,2,2,2,2,2,2,2,1,1,2,3,4,3,4,7,4,3,4,3,2,1,1,2,2,2,2,2,2,2,2,2,2,2,2,1
%N A356300 Square array read by antidiagonals. A(n,k) is the nearest common ancestor of n and k in the binary tree depicted in A253563.
%C A356300 Array is symmetric and is read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ... .
%C A356300 Also the nearest common ancestor of n and k in the tree depicted in A253565 (the mirror image of the A253563-tree).
%H A356300 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%e A356300 The top left 21x21 corner of the array:
%e A356300 n/k | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
%e A356300 -----+----------------------------------------------------------------------------
%e A356300 1 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A356300 2 | 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
%e A356300 3 | 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3,
%e A356300 4 | 1, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2,
%e A356300 5 | 1, 2, 3, 2, 5, 2, 5, 2, 3, 2, 5, 2, 5, 2, 3, 2, 5, 2, 5, 2, 3,
%e A356300 6 | 1, 2, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2,
%e A356300 7 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 7, 2, 7, 2, 3, 2, 7, 2, 7, 2, 3,
%e A356300 8 | 1, 2, 2, 4, 2, 4, 2, 8, 2, 4, 2, 8, 2, 4, 2, 8, 2, 4, 2, 8, 2,
%e A356300 9 | 1, 2, 3, 2, 3, 2, 3, 2, 9, 2, 3, 2, 3, 2, 9, 2, 3, 2, 3, 2, 9,
%e A356300 10 | 1, 2, 2, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 10, 2, 4, 2, 6, 2, 4, 2,
%e A356300 11 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 11, 2, 3, 2, 11, 2, 11, 2, 3,
%e A356300 12 | 1, 2, 2, 4, 2, 4, 2, 8, 2, 4, 2, 12, 2, 4, 2, 8, 2, 4, 2, 12, 2,
%e A356300 13 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 13, 2, 13, 2, 3,
%e A356300 14 | 1, 2, 2, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 14, 2, 4, 2, 6, 2, 4, 2,
%e A356300 15 | 1, 2, 3, 2, 3, 2, 3, 2, 9, 2, 3, 2, 3, 2, 15, 2, 3, 2, 3, 2, 15,
%e A356300 16 | 1, 2, 2, 4, 2, 4, 2, 8, 2, 4, 2, 8, 2, 4, 2, 16, 2, 4, 2, 8, 2,
%e A356300 17 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 17, 2, 3,
%e A356300 18 | 1, 2, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2, 6, 2, 4, 2, 18, 2, 4, 2,
%e A356300 19 | 1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2, 3,
%e A356300 20 | 1, 2, 2, 4, 2, 4, 2, 8, 2, 4, 2, 12, 2, 4, 2, 8, 2, 4, 2, 20, 2,
%e A356300 21 | 1, 2, 3, 2, 3, 2, 3, 2, 9, 2, 3, 2, 3, 2, 15, 2, 3, 2, 3, 2, 21,
%e A356300 .
%e A356300 A(3,6) = A(6,3) = 2 because the nearest common ancestor of 3 and 6 in the tree described in A253563 (and in A253565) is 2.
%e A356300 A(4,6) = A(6,4) = 4 because 6 occurs as a descendant of 4 in A253563-tree, thus their nearest common ancestor is 4 itself.
%o A356300 (PARI)
%o A356300 up_to = 105;
%o A356300 A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
%o A356300 A356300sq(x,y) = if(1==x||1==y,1, my(lista=List([]), i, k=x, stemvec, stemlen, h=y); while(k>1, listput(lista,k); k = A253553(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,h))>0, return(stemvec[i])); h = A253553(h)));
%o A356300 A356300list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A356300sq(col,(a-(col-1))))); (v); };
%o A356300 v356300 = A356300list(up_to);
%o A356300 A356300(n) = v356300[n];
%Y A356300 Cf. A253553, A253563, A253565, A356301.
%Y A356300 Cf. also A348041.
%K A356300 nonn,tabl
%O A356300 1,5
%A A356300 _Antti Karttunen_, Aug 03 2022