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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.

%I A379500 #11 Jan 03 2025 09:32:28
%S A379500 6,28,12,2,117,30,120,40,775,56,45,1080,1680,2793,132,21,672,19500,
%T A379500 7392,16093,182,84,390,3960,137200,24024,30927,306,496,176,43400,208,
%U A379500 1948584,55692,88723,380,78,9801,5460,368676,40392,5228860,116280,137541,552,210,9300,488125,17136,2928926,69160,25645860,209760,292537,870
%N 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.
%H A379500 Antti Karttunen, <a href="/A379500/b379500.txt">Table of n, a(n) for n = 1..11325; the first 150 antidiagonals of array</a>
%H A379500 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A379500 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A379500 A(n, k) = A341605(n, k) * A341606(n, k).
%F A379500 A(n, k) = A379499(n, k) / (A355925(n, k)^2).
%e A379500 The top left corner of the array:
%e A379500 k=|   1      2      3        4      5        6      7          8        9       10
%e A379500 2k|   2      4      6        8     10       12     14         16       18       20
%e A379500 --+---------------------------------------------------------------------------------
%e A379500 1 |   6,    28,     2,     120,    45,      21,    84,       496,      78,     210,
%e A379500 2 |  12,   117,    40,    1080,   672,     390,   176,      9801,    9300,    6552,
%e A379500 3 |  30,   775,  1680,   19500,  3960,   43400,  5460,    488125,   83790,  102300,
%e A379500 4 |  56,  2793,  7392,  137200,   208,  368676, 17136,   6725201,   18392,   10374,
%e A379500 5 | 132, 16093, 24024, 1948584, 40392, 2928926, 50160, 235793305, 4082364, 4924458,
%o A379500 (PARI)
%o A379500 up_to = 55;
%o A379500 A249670(n) = { my(ab = sigma(n)/n); numerator(ab)*denominator(ab); };
%o A379500 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));
%o A379500 A379500sq(row,col) = A249670(A246278sq(row,col));
%o A379500 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); };
%o A379500 v379500 = A379500list(up_to);
%o A379500 A379500(n) = v379500[n];
%Y A379500 Elementwise product of arrays A341605 and A341606.
%Y A379500 Cf. A246278, A249670, A355925, A379499.
%Y A379500 Cf. A036690 (leftmost column), A361468 (even bisection gives row 2).
%K A379500 nonn,tabl
%O A379500 1,1
%A A379500 _Antti Karttunen_, Jan 02 2025