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A355927
Square array A(n, k) = sigma(A246278(n, k)), read by falling antidiagonals.
11
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.
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. A008864 (column 1), A062731 (row 1).
Cf. also A341605, A355925, A355941.
Sequence in context: A066538 A352709 A216627 * A365724 A112305 A231396
KEYWORD
nonn,tabl,look
AUTHOR
Antti Karttunen, Jul 22 2022
STATUS
approved