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

Author

Antti Karttunen, Jul 22 2022

Keywords

• nonn
• tabl
• look

Comments

Each column is strictly monotonic.

Examples

			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.
		

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)

Crossrefs

Cf. A000203, A246278.

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

Cf. also A341605, A355925, A355941.

Programs

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];

Formula

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

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