A379220 - OEIS

%I #11 Dec 22 2024 09:07:57

%S 1,13,13,31,169,31,57,403,403,57,121,741,961,741,121,133,1573,1767,

%T 1767,1573,133,183,1729,3751,3249,3751,1729,183,403,2379,4123,6897,

%U 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 Square array A(n, k) = sigma((2n-1)^2) * sigma((2k-1)^2), read by antidiagonals.

%C Array is symmetric.

%H Antti Karttunen, <a href="/A379220/b379220.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F A(n, k) = A379223(n) * A379223(k).

%F A(n, k) = A000203(A016754(n-1)) * A000203(A016754(k-1)). [NB: A016754 uses 0-based indexing]

%e The top left corner of the array:

%e    n\k   |    1      2      3      4       5       6       7       8       9

%e (*2-1)^2 |    1      9     25     49      81     121     169     225     289

%e ---------+-------------------------------------------------------------------

%e    1   1 |    1,    13,    31,    57,    121,    133,    183,    403,    307,

%e    2   9 |   13,   169,   403,   741,   1573,   1729,   2379,   5239,   3991,

%e    3  25 |   31,   403,   961,  1767,   3751,   4123,   5673,  12493,   9517,

%e    4  49 |   57,   741,  1767,  3249,   6897,   7581,  10431,  22971,  17499,

%e    5  81 |  121,  1573,  3751,  6897,  14641,  16093,  22143,  48763,  37147,

%e    6 121 |  133,  1729,  4123,  7581,  16093,  17689,  24339,  53599,  40831,

%e    7 169 |  183,  2379,  5673, 10431,  22143,  24339,  33489,  73749,  56181,

%e    8 225 |  403,  5239, 12493, 22971,  48763,  53599,  73749, 162409, 123721,

%e    9 289 |  307,  3991,  9517, 17499,  37147,  40831,  56181, 123721,  94249,

%e   10 361 |  381,  4953, 11811, 21717,  46101,  50673,  69723, 153543, 116967,

%e   11 441 |  741,  9633, 22971, 42237,  89661,  98553, 135603, 298623, 227487,

%e   12 529 |  553,  7189, 17143, 31521,  66913,  73549, 101199, 222859, 169771,

%e   13 625 |  781, 10153, 24211, 44517,  94501, 103873, 142923, 314743, 239767,

%e   14 729 | 1093, 14209, 33883, 62301, 132253, 145369, 200019, 440479, 335551,

%e   15 841 |  871, 11323, 27001, 49647, 105391, 115843, 159393, 351013, 267397,

%e   16 961 |  993, 12909, 30783, 56601, 120153, 132069, 181719, 400179, 304851,

%o (PARI)

%o up_to = 66;

%o A379220sq(x,y) = (sigma((x+x-1)^2) * sigma((y+y-1)^2));

%o 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 v379220 = A379220list(up_to);

%o A379220(n) = v379220[n];

%Y Cf. A000203, A016754.

%Y Cf. A379223 (the first row and the first column).

%Y Cf. also A379221.

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Dec 22 2024