A372563 Square array A(n, k) = A246278(1+n, k) - sigma(A246278(n, k)), read by falling antidiagonals, where A246278 is the prime shift array.
0, 2, 1, 3, 12, 1, 12, 11, 18, 3, 3, 85, 29, 64, 1, 17, 23, 187, 47, 36, 3, 9, 97, 19, 931, 53, 106, 1, 50, 17, 291, 75, 733, 71, 54, 3, 36, 504, 35, 889, 31, 2533, 77, 148, 5, 21, 121, 1620, 65, 1011, 111, 1639, 187, 288, 1, 3, 171, 505, 11840, 59, 2197, 119, 4927, 179, 90, 5
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, 2, 3, 12, 3, 17, 9, 50, 36, 21, 3, 75, 2 | 1, 12, 11, 85, 23, 97, 17, 504, 121, 171, 29, 635, 3 | 1, 18, 29, 187, 19, 291, 35, 1620, 505, 265, 25, 2525, 4 | 3, 64, 47, 931, 75, 889, 65, 11840, 795, 1259, 93, 12503, 5 | 1, 36, 53, 733, 31, 1011, 59, 12456, 1561, 817, 89, 16853, 6 | 3, 106, 71, 2533, 111, 2197, 157, 52580, 1839, 2987, 107, 50507, 7 | 1, 54, 77, 1639, 119, 2163, 49, 41580, 3193, 3101, 127, 53357, 8 | 3, 148, 187, 4927, 113, 6197, 211, 142280, 8283, 4969, 183, 179083, 9 | 5, 288, 179, 11669, 305, 9481, 277, 414720, 6965, 13421, 239, 374459, 10 | 1, 90, 187, 4531, 131, 7685, 73, 190980, 12649, 6303, 137, 293947, 11 | 5, 376, 301, 19869, 247, 18395, 331, 919856, 17173, 17161, 425, 906981, 12 | 3, 274, 167, 16861, 255, 13189, 349, 899540, 10335, 17099, 367, 777083,
Links
Crossrefs
Programs
-
PARI
up_to = 66; 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)); A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; A286385(n) = (A003961(n)-sigma(n)); A372563sq(row,col) = A286385(A246278sq(row,col)); A372563list(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] = A372563sq(col,(a-(col-1))))); (v); }; v372563 = A372563list(up_to); A372563(n) = v372563[n];