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 A351381 #65 Apr 09 2022 06:13:16
%S A351381 4,9,8,16,18,12,25,32,27,16,36,50,48,36,20,49,72,75,64,45,24,64,98,
%T A351381 108,100,80,54,28,81,128,147,144,125,96,63,32,100,162,192,196,180,150,
%U A351381 112,72,36,121,200,243,256,245,216,175,128,81,40,144,242,300,324,320,294,252,200,144,90,44
%N A351381 Table read by downward antidiagonals: T(n,k) = n*(k+1)^2.
%C A351381 When m and k are both positive integers and k | m, with m/k = n, then T(n,k) = S(m,k) = (m+k) + (m-k) + (m*k) + (m/k) = S(n*k,k) = n*(k+1)^2, problem proposed by Yakov Perelman.
%C A351381 All terms are nonsquarefree (A013929).
%D A351381 I. Perelman, L'Algèbre Récréative, Chapitre IV, Les équations de Diophante, Deux nombres et quatre opérations, Editions en langues étrangères, Moscou, 1959, pp. 101-102.
%D A351381 Ya. I. Perelman, Algebra Can Be Fun, Chapter IV, Diophantine Equations, Two numbers and four operations, Mir Publishers Moscow, 1979, pp. 131-132.
%H A351381 Ya. I. Perelman, <a href="https://mirtitles.org/2012/05/23/yakov-perelman-algebra-can-be-fun/">Algebra Can Be Fun</a>, Chapter IV, Diophantine Equations, Two numbers and four operations, Mir Publishers Moscow, 1979, pp. 131-132.
%H A351381 Wikipedia, <a href="https://en.wikipedia.org/wiki/Yakov_Perelman">Yakov Perelman</a>.
%F A351381 T(n,k) = n*(k+1)^2.
%F A351381 T(n,n) = (n+1)^3 - (n+1)^2 = A045991(n+1) for n >= 1.
%F A351381 G.f.: x*(1 + y)/((1 - x)^2*(1 - y)^3). - _Stefano Spezia_, Mar 31 2022
%e A351381 Table begins:
%e A351381 n \ k | 1 2 3 4 5 6 7 8 9 10
%e A351381 ----------------------------------------------------------------------------
%e A351381 1 | 4 9 16 25 36 49 64 81 100 121
%e A351381 2 | 8 18 32 50 72 98 128 162 200 242
%e A351381 3 | 12 27 48 75 108 147 192 243 300 363
%e A351381 4 | 16 36 64 100 144 196 256 324 400 484
%e A351381 5 | 20 45 80 125 180 245 320 405 500 605
%e A351381 6 | 24 54 96 150 216 294 384 486 600 726
%e A351381 7 | 28 63 112 175 252 343 448 567 700 847
%e A351381 8 | 32 72 128 200 288 392 512 648 800 968
%e A351381 9 | 36 81 144 225 324 441 576 729 900 1089
%e A351381 10 | 40 90 160 250 360 490 640 810 1000 1210
%e A351381 ............................................................................
%e A351381 T(3,4) = 75 = 3*(4+1)^2 corresponds to S(3*4,4) = S(12,4) = (12+4) + (12-4) + (12*4) + 12/4 = 75.
%e A351381 S(10,5) = (10+5) + (10-5) + (10*5) + (10/5) = T(10/5,5) = T(2,5) = 72.
%t A351381 T[n_, k_] := n*(k + 1)^2; Table[T[k, n - k + 1], {n, 1, 11}, {k, 1, n}] // Flatten (* _Amiram Eldar_, Mar 29 2022 *)
%Y A351381 Cf. A013929.
%Y A351381 Cf. A000290 \ {0,1} (row 1), A001105 \ {0,2} (row 2), A033428 \ {0,3} (row 3), A016742 \ {0,4} (row 4), A033429 \ {0,5} (row 5), A033581 \ {0,6} (row 6).
%Y A351381 Cf. A008586 \ {0} (column 1), A008591 \ {0} (column 2), A008598 \ {0} (column 3), A008607 \ {0} (column 4), A044102 \ {0} (column 5).
%Y A351381 Cf. A045991 \ {0} (diagonal).
%K A351381 nonn,tabl
%O A351381 1,1
%A A351381 _Bernard Schott_, Mar 28 2022