A379008 Square array A(n, k) = A294898(A246278(n, k)), read by falling antidiagonals; Difference A005187(n)-A000203(n) applied to the prime shift array.
0, 0, 0, -2, 3, 2, 0, 2, 16, 3, 0, 10, 19, 38, 7, -6, 7, 88, 54, 104, 9, 1, 8, 33, 280, 113, 151, 14, 0, 16, 96, 65, 1192, 184, 268, 15, -5, 38, 44, 389, 152, 2009, 282, 336, 18, -4, 22, 464, 88, 1279, 207, 4600, 388, 502, 24, 5, 16, 142, 1996, 174, 2445, 345, 6470, 608, 806, 25, -14, 18, 174, 623, 13170, 257, 4834, 497, 11605, 833, 924, 33
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 | 0, 0, -2, 0, 0, -6, 1, 0, -5, -4, 5, -14, 2 | 0, 3, 2, 10, 7, 8, 16, 38, 22, 16, 18, 26, 3 | 2, 16, 19, 88, 33, 96, 44, 464, 142, 174, 58, 495, 4 | 3, 38, 54, 280, 65, 389, 88, 1996, 623, 469, 103, 2737, 5 | 7, 104, 113, 1192, 152, 1279, 174, 13170, 1516, 1717, 211, 14102, 6 | 9, 151, 184, 2009, 207, 2445, 257, 26172, 3208, 2756, 328, 31850, 7 | 14, 268, 282, 4600, 345, 4834, 439, 78295, 5406, 5916, 473, 82285, 8 | 15, 336, 388, 6470, 497, 7455, 533, 123071, 9035, 9501, 638, 141745, 9 | 18, 502, 608, 11605, 653, 14081, 784, 267115, 17773, 15097, 870, 324077, Here 0's occur also after the first row. For example column 30, which corresponds with numbers 60, 315, 1925, 7007, 26741, ..., begins as -52, 0, 868, 4428, 19958, etc. See also A295296.
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Programs
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PARI
up_to = 11325; \\ = binomial(150+1,2) A005187(n) = { my(s=n); while(n>>=1, s+=n); s; }; A294898(n) = (A005187(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)); A379008sq(row,col) = A294898(A246278sq(row,col)); A379008list(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] = A379008sq(col,(a-(col-1))))); (v); }; v379008 = A379008list(up_to); A379008(n) = v379008[n];
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