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 A379220 #11 Dec 22 2024 09:07:57
%S A379220 1,13,13,31,169,31,57,403,403,57,121,741,961,741,121,133,1573,1767,
%T A379220 1767,1573,133,183,1729,3751,3249,3751,1729,183,403,2379,4123,6897,
%U A379220 6897,4123,2379,403,307,5239,5673,7581,14641,7581,5673,5239,307,381,3991,12493,10431,16093,16093,10431,12493,3991,381,741,4953,9517,22971,22143,17689,22143,22971,9517,4953,741
%N A379220 Square array A(n, k) = sigma((2n-1)^2) * sigma((2k-1)^2), read by antidiagonals.
%C A379220 Array is symmetric.
%H A379220 Antti Karttunen, <a href="/A379220/b379220.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals</a>
%H A379220 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379220 A(n, k) = A379223(n) * A379223(k).
%F A379220 A(n, k) = A000203(A016754(n-1)) * A000203(A016754(k-1)). [NB: A016754 uses 0-based indexing]
%e A379220 The top left corner of the array:
%e A379220 n\k | 1 2 3 4 5 6 7 8 9
%e A379220 (*2-1)^2 | 1 9 25 49 81 121 169 225 289
%e A379220 ---------+-------------------------------------------------------------------
%e A379220 1 1 | 1, 13, 31, 57, 121, 133, 183, 403, 307,
%e A379220 2 9 | 13, 169, 403, 741, 1573, 1729, 2379, 5239, 3991,
%e A379220 3 25 | 31, 403, 961, 1767, 3751, 4123, 5673, 12493, 9517,
%e A379220 4 49 | 57, 741, 1767, 3249, 6897, 7581, 10431, 22971, 17499,
%e A379220 5 81 | 121, 1573, 3751, 6897, 14641, 16093, 22143, 48763, 37147,
%e A379220 6 121 | 133, 1729, 4123, 7581, 16093, 17689, 24339, 53599, 40831,
%e A379220 7 169 | 183, 2379, 5673, 10431, 22143, 24339, 33489, 73749, 56181,
%e A379220 8 225 | 403, 5239, 12493, 22971, 48763, 53599, 73749, 162409, 123721,
%e A379220 9 289 | 307, 3991, 9517, 17499, 37147, 40831, 56181, 123721, 94249,
%e A379220 10 361 | 381, 4953, 11811, 21717, 46101, 50673, 69723, 153543, 116967,
%e A379220 11 441 | 741, 9633, 22971, 42237, 89661, 98553, 135603, 298623, 227487,
%e A379220 12 529 | 553, 7189, 17143, 31521, 66913, 73549, 101199, 222859, 169771,
%e A379220 13 625 | 781, 10153, 24211, 44517, 94501, 103873, 142923, 314743, 239767,
%e A379220 14 729 | 1093, 14209, 33883, 62301, 132253, 145369, 200019, 440479, 335551,
%e A379220 15 841 | 871, 11323, 27001, 49647, 105391, 115843, 159393, 351013, 267397,
%e A379220 16 961 | 993, 12909, 30783, 56601, 120153, 132069, 181719, 400179, 304851,
%o A379220 (PARI)
%o A379220 up_to = 66;
%o A379220 A379220sq(x,y) = (sigma((x+x-1)^2) * sigma((y+y-1)^2));
%o A379220 A379220list(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] = A379220sq(col,(a-(col-1))))); (v); };
%o A379220 v379220 = A379220list(up_to);
%o A379220 A379220(n) = v379220[n];
%Y A379220 Cf. A000203, A016754.
%Y A379220 Cf. A379223 (the first row and the first column).
%Y A379220 Cf. also A379221.
%K A379220 nonn,tabl
%O A379220 1,2
%A A379220 _Antti Karttunen_, Dec 22 2024