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%I A341627 #15 Feb 20 2021 07:53:17
%S A341627 9,63,10,5,325,21,81,7,1519,22,189,1250,11,363,78,35,220,13377,52,
%T A341627 22477,119,33,455,117,66550,34,52887,171,2511,260,4774,374,804102,133,
%U A341627 110827,115,325,6875,833,2574,6669,584647,69,201549,116,1323,3038,1875181,627,205751,13685,1790199,58,465073,465
%N A341627 Square array A(n,k) = A341527(A246278(n,k)), read by falling antidiagonals; denominators of the columnwise first quotients of A341605/A341606.
%H A341627 Index entries for sequences computed from indices in prime factorization
%H A341627 Index entries for sequences related to sigma(n)
%F A341627 A(n,k) = A341527(A246278(n,k)), where A341527(n) is the denominator of the ratio (n * sigma(A003961(n))) / (sigma(n) * A003961(n)), i.e., of A341528(n)/A341529(n).
%F A341627 For all n, k, A(n,k) > A341626(n, k).
%e A341627 The top left corner of the array:
%e A341627 n = 1 2 3 4 5 6 7 8 9
%e A341627 2n = 2 4 6 8 10 12 14 16 18
%e A341627 ----+--------------------------------------------------------------------------
%e A341627 1 | 9, 63, 5, 81, 189, 35, 33, 2511, 325,
%e A341627 2 | 10, 325, 7, 1250, 220, 455, 260, 6875, 3038,
%e A341627 3 | 21, 1519, 11, 13377, 117, 4774, 833, 1875181, 1089,
%e A341627 4 | 22, 363, 52, 66550, 374, 2574, 627, 41009441, 6422,
%e A341627 5 | 78, 22477, 34, 804102, 6669, 205751, 1495, 459974905, 317322,
%e A341627 6 | 119, 52887, 133, 584647, 13685, 531981, 13804, 2584223261, 775789,
%e A341627 7 | 171, 110827, 69, 1790199, 9918, 670795, 15903, 11564815861, 1813941,
%e A341627 8 | 115, 201549, 58, 2202227, 17825, 1016508, 34040, 38495207801, 2325365,
%e A341627 9 | 116, 465073, 93, 5170468, 68672, 7457205, 90364, 206922836641, 3348124,
%e A341627 etc.
%o A341627 (PARI)
%o A341627 up_to = 105;
%o A341627 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 A341627 A341627sq(row,col) = A341527(A246278sq(row,col));
%o A341627 A341627list(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] = A341627sq(col,(a-(col-1))))); (v); };
%o A341627 v341627 = A341627list(up_to);
%o A341627 A341627(n) = v341627[n];
%Y A341627 Cf. A246278, A341605, A341606, A341527.
%Y A341627 Cf. A341626 (numerators), A341628 (the greatest prime factor of these terms).
%K A341627 nonn,frac,tabl
%O A341627 1,1
%A A341627 _Antti Karttunen_, Feb 16 2021
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