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A378979
Square array A(n, k) = 2*A246278(n, k) - sigma(A246278(n, k)), read by falling antidiagonals. Deficiency applied to the the prime shift array.
0
1, 1, 2, 0, 5, 4, 1, 6, 19, 6, 2, 14, 22, 41, 10, -4, 10, 94, 58, 109, 12, 4, 12, 38, 286, 118, 155, 16, 1, 18, 102, 70, 1198, 190, 271, 18, -3, 41, 46, 394, 158, 2014, 286, 341, 22, -2, 26, 469, 94, 1284, 214, 4606, 394, 505, 28, 8, 22, 148, 2001, 178, 2452, 350, 6478, 614, 811, 30, -12, 22, 178, 630, 13177, 262, 4842, 502, 11614, 838, 929, 36
OFFSET
1,3
COMMENTS
Each column is strictly increasing.
For all k >= 1, A(1+A378985(k), k) > 0, and it is the topmost positive number of the column k.
FORMULA
A(n, k) = A033879(A246278(n, k)) = 2*A246278(n, k) - A355927(n, k).
A(n, k) = A372563(n,k) - A372562(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 | 1, 1, 0, 1, 2, -4, 4, 1, -3, -2, 8, -12,
2 | 2, 5, 6, 14, 10, 12, 18, 41, 26, 22, 22, 30,
3 | 4, 19, 22, 94, 38, 102, 46, 469, 148, 178, 62, 502,
4 | 6, 41, 58, 286, 70, 394, 94, 2001, 630, 476, 106, 2746,
5 | 10, 109, 118, 1198, 158, 1284, 178, 13177, 1522, 1720, 218, 14110,
6 | 12, 155, 190, 2014, 214, 2452, 262, 26181, 3216, 2762, 334, 31858,
7 | 16, 271, 286, 4606, 350, 4842, 446, 78301, 5416, 5926, 478, 82294,
PROG
(PARI)
up_to = 78;
A033879(n) = (n+n-sigma(n));
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));
A378979sq(row, col) = A033879(A246278sq(row, col));
A378979list(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] = A378979sq(col, (a-(col-1))))); (v); };
v378979 = A378979list(up_to);
A378979(n) = v378979[n];
CROSSREFS
Cf. A006093 (column 1), A306190 (column 2), A378978 (row 1), A378985 (row index of the topmost positive term in column n).
Cf. also arrays A341605, A341606 and A341607.
Cf. also A324055.
Sequence in context: A349950 A164976 A261745 * A083714 A215481 A262933
KEYWORD
sign,tabl,new
AUTHOR
Antti Karttunen, Dec 13 2024
STATUS
approved