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A341627 Square array A(n,k) = A341527(A246278(n,k)), read by falling antidiagonals; denominators of the columnwise first quotients of A341605/A341606.

%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 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A341627 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%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