A379220 Square array A(n, k) = sigma((2n-1)^2) * sigma((2k-1)^2), read by antidiagonals.

1, 13, 13, 31, 169, 31, 57, 403, 403, 57, 121, 741, 961, 741, 121, 133, 1573, 1767, 1767, 1573, 133, 183, 1729, 3751, 3249, 3751, 1729, 183, 403, 2379, 4123, 6897, 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

Offset

1,2

Comments

Array is symmetric.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals

Index entries for sequences related to sigma(n).

Formula

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

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

Example

The top left corner of the array:
   n\k   |    1      2      3      4       5       6       7       8       9
(*2-1)^2 |    1      9     25     49      81     121     169     225     289
---------+-------------------------------------------------------------------
   1   1 |    1,    13,    31,    57,    121,    133,    183,    403,    307,
   2   9 |   13,   169,   403,   741,   1573,   1729,   2379,   5239,   3991,
   3  25 |   31,   403,   961,  1767,   3751,   4123,   5673,  12493,   9517,
   4  49 |   57,   741,  1767,  3249,   6897,   7581,  10431,  22971,  17499,
   5  81 |  121,  1573,  3751,  6897,  14641,  16093,  22143,  48763,  37147,
   6 121 |  133,  1729,  4123,  7581,  16093,  17689,  24339,  53599,  40831,
   7 169 |  183,  2379,  5673, 10431,  22143,  24339,  33489,  73749,  56181,
   8 225 |  403,  5239, 12493, 22971,  48763,  53599,  73749, 162409, 123721,
   9 289 |  307,  3991,  9517, 17499,  37147,  40831,  56181, 123721,  94249,
  10 361 |  381,  4953, 11811, 21717,  46101,  50673,  69723, 153543, 116967,
  11 441 |  741,  9633, 22971, 42237,  89661,  98553, 135603, 298623, 227487,
  12 529 |  553,  7189, 17143, 31521,  66913,  73549, 101199, 222859, 169771,
  13 625 |  781, 10153, 24211, 44517,  94501, 103873, 142923, 314743, 239767,
  14 729 | 1093, 14209, 33883, 62301, 132253, 145369, 200019, 440479, 335551,
  15 841 |  871, 11323, 27001, 49647, 105391, 115843, 159393, 351013, 267397,
  16 961 |  993, 12909, 30783, 56601, 120153, 132069, 181719, 400179, 304851,

Prog

(PARI)
up_to = 66;
A379220sq(x, y) = (sigma((x+x-1)^2) * sigma((y+y-1)^2));
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); };
v379220 = A379220list(up_to);
A379220(n) = v379220[n];

Crossrefs

Cf. A000203, A016754.

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

Cf. also A379221.

Sequence in context: A022347 A026907 A210475 * A304268 A214466 A302678

Adjacent sequences: A379217 A379218 A379219 * A379221 A379222 A379223

Keyword

nonn,tabl

Author

Antti Karttunen, Dec 22 2024

Status

approved