A379500 Square array A(n, k) = A249670(A246278(n, k)), read by falling antidiagonals; A249670(n) = A017665(n)*A017666(n), applied to the prime shift array.
6, 28, 12, 2, 117, 30, 120, 40, 775, 56, 45, 1080, 1680, 2793, 132, 21, 672, 19500, 7392, 16093, 182, 84, 390, 3960, 137200, 24024, 30927, 306, 496, 176, 43400, 208, 1948584, 55692, 88723, 380, 78, 9801, 5460, 368676, 40392, 5228860, 116280, 137541, 552, 210, 9300, 488125, 17136, 2928926, 69160, 25645860, 209760, 292537, 870
Offset: 1
Examples
The top left corner of the array: k=| 1 2 3 4 5 6 7 8 9 10 2k| 2 4 6 8 10 12 14 16 18 20 --+--------------------------------------------------------------------------------- 1 | 6, 28, 2, 120, 45, 21, 84, 496, 78, 210, 2 | 12, 117, 40, 1080, 672, 390, 176, 9801, 9300, 6552, 3 | 30, 775, 1680, 19500, 3960, 43400, 5460, 488125, 83790, 102300, 4 | 56, 2793, 7392, 137200, 208, 368676, 17136, 6725201, 18392, 10374, 5 | 132, 16093, 24024, 1948584, 40392, 2928926, 50160, 235793305, 4082364, 4924458,
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Crossrefs
Programs
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PARI
up_to = 55; A249670(n) = { my(ab = sigma(n)/n); numerator(ab)*denominator(ab); }; 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)); A379500sq(row,col) = A249670(A246278sq(row,col)); A379500list(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] = A379500sq(col,(a-(col-1))))); (v); }; v379500 = A379500list(up_to); A379500(n) = v379500[n];
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