A355927 Square array A(n, k) = sigma(A246278(n, k)), read by falling antidiagonals.

3, 7, 4, 12, 13, 6, 15, 24, 31, 8, 18, 40, 48, 57, 12, 28, 32, 156, 96, 133, 14, 24, 78, 72, 400, 168, 183, 18, 31, 48, 248, 112, 1464, 252, 307, 20, 39, 121, 84, 684, 216, 2380, 360, 381, 24, 42, 124, 781, 144, 1862, 280, 5220, 480, 553, 30, 36, 104, 342, 2801, 240, 3294, 432, 7240, 720, 871, 32, 60, 56, 372, 1064, 16105, 336, 6140, 600, 12720, 960, 993, 38

Offset

1,1

Comments

Each column is strictly monotonic.

Links

Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 antidiagonals

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

A(n, k) = A000203(A246278(n, k)).

A(n, k) = A341605(n, k) * A355925(n, k).

Example

The top left corner of the array:
   k=  1    2    3      4    5      6    7       8      9     10    11      12
  2k=  2    4    6      8   10     12   14      16     18     20    22      24
----+--------------------------------------------------------------------------
  1 |  3,   7,  12,    15,  18,    28,  24,     31,    39,    42,   36,     60,
  2 |  4,  13,  24,    40,  32,    78,  48,    121,   124,   104,   56,    240,
  3 |  6,  31,  48,   156,  72,   248,  84,    781,   342,   372,  108,   1248,
  4 |  8,  57,  96,   400, 112,   684, 144,   2801,  1064,   798,  160,   4800,
  5 | 12, 133, 168,  1464, 216,  1862, 240,  16105,  2196,  2394,  288,  20496,
  6 | 14, 183, 252,  2380, 280,  3294, 336,  30941,  4298,  3660,  420,  42840,
  7 | 18, 307, 360,  5220, 432,  6140, 540,  88741,  6858,  7368,  576, 104400,
  8 | 20, 381, 480,  7240, 600,  9144, 640, 137561, 11060, 11430,  760, 173760,
  9 | 24, 553, 720, 12720, 768, 16590, 912, 292561, 20904, 17696, 1008, 381600,
Note: See A355941 for the corresponding numbers in A246278 at which points the value in this array divides the term immediately below.

Prog

(PARI)
up_to = 105;
A246278sq(row, col) = if(1==row, 2*col, my(f = factor(2*col)); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])+(row-1))); factorback(f));
A355927sq(row, col) = sigma(A246278sq(row, col));
A355927list(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] = A355927sq(col, (a-(col-1))))); (v); };
v355927 = A355927list(up_to);
A355927(n) = v355927[n];

Crossrefs

Cf. A000203, A246278.

Cf. A008864 (column 1), A062731 (row 1).

Cf. also A341605, A355925, A355941.

Sequence in context: A066538 A352709 A216627 * A365724 A112305 A231396

Adjacent sequences: A355924 A355925 A355926 * A355928 A355929 A355930

Keyword

nonn,tabl,look

Author

Antti Karttunen, Jul 22 2022

Status

approved