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%I #29 Jan 08 2019 08:38:45
%S 1,3,2,4,6,3,7,8,9,4,6,14,12,12,5,12,12,21,16,15,6,8,24,18,28,20,18,7,
%T 15,16,36,24,35,24,21,8,13,30,24,48,30,42,28,24,9,18,26,45,32,60,36,
%U 49,32,27,10,12,36,39,60,40,72,42,56,36,30,11,28,24,54,52,75,48,84,48,63,40,33,12
%N Square array read by antidiagonals upwards: T(n,k) = k*sigma(n), n >= 1, k >= 1.
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e The corner of the square array begins:
%e A000203 A074400 A272027 A239050 A274535 A274536 A319527 A319528
%e A000027: 1, 2, 3, 4, 5, 6, 7, 8, ...
%e A008585: 3, 6, 9, 12, 15, 18, 21, 24, ...
%e A008586: 4, 8, 12, 16, 20, 24, 28, 32, ...
%e A008589: 7, 14, 21, 28, 35, 42, 49, 56, ...
%e A008588: 6, 12, 18, 24, 30, 36, 42, 48, ...
%e A008594: 12, 24, 36, 48, 60, 72, 84, 96, ...
%e A008590: 8, 16, 24, 32, 40, 48, 56, 64, ...
%e A008597: 15, 30, 45, 60, 75, 90, 105, 120, ...
%e A008595: 13, 26, 39, 52, 65, 78, 91, 104, ...
%e A008600: 18, 36, 54, 72, 90, 108, 126, 144, ...
%e ...
%p with(numtheory): T:=(n,k)->k*sigma(n-k+1): seq(seq(T(n,k),k=1..n),n=1..12); # _Muniru A Asiru_, Jan 01 2019
%t Table[k DivisorSigma[1, #] &[m - k + 1], {m, 12}, {k, m}] // Flatten (* _Michael De Vlieger_, Dec 31 2018 *)
%o (GAP) T:=Flat(List([1..12],n->List([1..n],k->k*Sigma(n-k+1))));; Print(T); # _Muniru A Asiru_, Jan 01 2019
%Y Another version of A274824.
%Y Antidiagonal sums give A175254.
%Y Main diagonal gives A064987.
%Y Row n lists the multiples of A000203(n).
%Y Row 1 is A000027.
%Y Initial zeros should be omitted in the following sequences related to the rows of the array:
%Y Row 2-5: A008585, A008586, A008589, A008588.
%Y Rows 6 and 11: A008594.
%Y Rows 7-9: A008590, A008597, A008595.
%Y Rows 10 and 17: A008600.
%Y Rows 12-13: A135628, A008596.
%Y Rows 14, 15 and 23: A008606.
%Y Rows 16 and 25: A135631.
%Y (Note that in the OEIS there are many other sequences that are also rows of this square array.)
%Y Cf. A000203, A237593, A319526.
%K nonn,tabl,easy
%O 1,2
%A _Omar E. Pol_, Sep 22 2018
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