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 A342765 #14 Apr 04 2021 06:22:23 %S A342765 1,2,2,3,2,3,4,3,3,4,5,4,3,4,5,6,5,6,6,5,6,7,6,5,4,5,6,7,8,7,6,10,10, %T A342765 6,7,8,9,8,7,6,5,6,7,8,9,10,9,12,14,10,10,14,12,9,10,11,10,9,8,7,6,7, %U A342765 8,9,10,11,12,11,10,9,20,14,14,20,9,10,11,12 %N A342765 Array T(n, k), n, k > 0, read by antidiagonals; T(n, k) = max(A006530(n), A006530(k)) * T(n/A006530(n), k/A006530(k)) with T(1, 1) = 1. %C A342765 To compute T(n, k): %C A342765 - write the prime factors of n and of k in ascending order with multiplicities on two lines, right aligned, %C A342765 - take the largest prime number in each column and multiply back, %C A342765 - for example, for T(12, 14): %C A342765 12 -> 2 2 3 %C A342765 14 -> 2 7 %C A342765 ----- %C A342765 2 2 7 -> 28 = T(12, 14) %C A342765 This sequence is closely related to lunar addition (A087061): %C A342765 - let n and k be two p-smooth numbers, %C A342765 - let f be the function that associates to a p-smooth number, say m, the unique number whose (p+1)-base digits are prime, nondecreasing and whose product is m, %C A342765 - let g be the inverse of f, %C A342765 - then for any p-smooth numbers n and k, T(n, k) = g(f(n) "+" f(k)) where "+" denotes lunar addition in base p+1, %C A342765 - see A342767 for the corresponding multiplication. %H A342765 Rémy Sigrist, <a href="/A342765/b342765.txt">Table of n, a(n) for n = 1..10011</a> %H A342765 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a> %F A342765 T(n, k) = T(k, n). %F A342765 T(m, T(n, k)) = T(T(m, n), k). %F A342765 T(n, 1) = n. %F A342765 T(n, n) = n. %F A342765 A001222(T(n, k)) = max(A001222(n), A001222(k)). %F A342765 A006530(T(n, k)) = max(A006530(n), A006530(k)). %e A342765 Array T(n, k) begins: %e A342765 n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 %e A342765 ---+-------------------------------------------------------- %e A342765 1| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 %e A342765 2| 2 2 3 4 5 6 7 8 9 10 11 12 13 14 %e A342765 3| 3 3 3 6 5 6 7 12 9 10 11 12 13 14 %e A342765 4| 4 4 6 4 10 6 14 8 9 10 22 12 26 14 %e A342765 5| 5 5 5 10 5 10 7 20 15 10 11 20 13 14 %e A342765 6| 6 6 6 6 10 6 14 12 9 10 22 12 26 14 %e A342765 7| 7 7 7 14 7 14 7 28 21 14 11 28 13 14 %e A342765 8| 8 8 12 8 20 12 28 8 18 20 44 12 52 28 %e A342765 9| 9 9 9 9 15 9 21 18 9 15 33 18 39 21 %e A342765 10| 10 10 10 10 10 10 14 20 15 10 22 20 26 14 %e A342765 11| 11 11 11 22 11 22 11 44 33 22 11 44 13 22 %e A342765 12| 12 12 12 12 20 12 28 12 18 20 44 12 52 28 %e A342765 13| 13 13 13 26 13 26 13 52 39 26 13 52 13 26 %e A342765 14| 14 14 14 14 14 14 14 28 21 14 22 28 26 14 %o A342765 (PARI) gpf(n) = if (n==1, 1, my (p=factor(n)[,1]~); p[#p]) %o A342765 T(n, k) = if (n==1 || k==1, max(n, k), my (p=gpf(n), q=gpf(k)); max(p, q)*T(n/p, k/q)) %Y A342765 Cf. A001222, A006530, A087061, A342766, A342767. %K A342765 nonn,tabl %O A342765 1,2 %A A342765 _Rémy Sigrist_, Apr 02 2021