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A355927
Square array A(n, k) = sigma(A246278(n, k)), read by falling antidiagonals.
9
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