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A355927 Square array A(n, k) = sigma(A246278(n, k)), read by falling antidiagonals.

%I A355927 #11 Jul 24 2022 10:45:35
%S A355927 3,7,4,12,13,6,15,24,31,8,18,40,48,57,12,28,32,156,96,133,14,24,78,72,
%T A355927 400,168,183,18,31,48,248,112,1464,252,307,20,39,121,84,684,216,2380,
%U A355927 360,381,24,42,124,781,144,1862,280,5220,480,553,30,36,104,342,2801,240,3294,432,7240,720,871,32,60,56,372,1064,16105,336,6140,600,12720,960,993,38
%N A355927 Square array A(n, k) = sigma(A246278(n, k)), read by falling antidiagonals.
%C A355927 Each column is strictly monotonic.
%H A355927 Antti Karttunen, <a href="/A355927/b355927.txt">Table of n, a(n) for n = 1..22155; the first 210 antidiagonals</a>
%H A355927 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A355927 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A355927 A(n, k) = A000203(A246278(n, k)).
%F A355927 A(n, k) = A341605(n, k) * A355925(n, k).
%e A355927 The top left corner of the array:
%e A355927    k=  1    2    3      4    5      6    7       8      9     10    11      12
%e A355927   2k=  2    4    6      8   10     12   14      16     18     20    22      24
%e A355927 ----+--------------------------------------------------------------------------
%e A355927   1 |  3,   7,  12,    15,  18,    28,  24,     31,    39,    42,   36,     60,
%e A355927   2 |  4,  13,  24,    40,  32,    78,  48,    121,   124,   104,   56,    240,
%e A355927   3 |  6,  31,  48,   156,  72,   248,  84,    781,   342,   372,  108,   1248,
%e A355927   4 |  8,  57,  96,   400, 112,   684, 144,   2801,  1064,   798,  160,   4800,
%e A355927   5 | 12, 133, 168,  1464, 216,  1862, 240,  16105,  2196,  2394,  288,  20496,
%e A355927   6 | 14, 183, 252,  2380, 280,  3294, 336,  30941,  4298,  3660,  420,  42840,
%e A355927   7 | 18, 307, 360,  5220, 432,  6140, 540,  88741,  6858,  7368,  576, 104400,
%e A355927   8 | 20, 381, 480,  7240, 600,  9144, 640, 137561, 11060, 11430,  760, 173760,
%e A355927   9 | 24, 553, 720, 12720, 768, 16590, 912, 292561, 20904, 17696, 1008, 381600,
%e A355927 Note: See A355941 for the corresponding numbers in A246278 at which points the value in this array divides the term immediately below.
%o A355927 (PARI)
%o A355927 up_to = 105;
%o A355927 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 A355927 A355927sq(row,col) = sigma(A246278sq(row,col));
%o A355927 A355927list(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] = A355927sq(col,(a-(col-1))))); (v); };
%o A355927 v355927 = A355927list(up_to);
%o A355927 A355927(n) = v355927[n];
%Y A355927 Cf. A000203, A246278.
%Y A355927 Cf. A008864 (column 1), A062731 (row 1).
%Y A355927 Cf. also A341605, A355925, A355941.
%K A355927 nonn,tabl,look
%O A355927 1,1
%A A355927 _Antti Karttunen_, Jul 22 2022