A378979 Square array A(n, k) = 2*A246278(n, k) - sigma(A246278(n, k)), read by falling antidiagonals. Deficiency applied to the prime shift array.
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
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 | 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,
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Crossrefs
Programs
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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];
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