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%I #19 Apr 29 2016 23:36:38
%S 1,2,3,3,6,4,5,9,8,7,7,15,12,14,6,11,21,20,21,12,12,13,33,28,35,18,24,
%T 8,17,39,44,49,30,36,16,15,19,51,52,77,42,60,24,30,13,23,57,68,91,66,
%U 84,40,45,26,18,29,69,76,119,78,132,56,75,39,36,12,31,87,92,133,102,156,88,105,65,54,24,28
%N Square array read by antidiagonals upwards in which T(n,k) is the product of the n-th noncomposite number and the sum of the divisors of k, n>=1, k>=1.
%F T(n,k) = A008578(n)*A000203(k), n>=1, k>=1.
%F T(n,k) = A272214(n-1,k), n>=2.
%e The corner of the square array begins:
%e 1, 3, 4, 7, 6, 12, 8, 15, 13, 18...
%e 2, 6, 8, 14, 12, 24, 16, 30, 26, 36...
%e 3, 9, 12, 21, 18, 36, 24, 45, 39, 54...
%e 5, 15, 20, 35, 30, 60, 40, 75, 65, 90...
%e 7, 21, 28, 49, 42, 84, 56, 105, 91, 126...
%e 11, 33, 44, 77, 66, 132, 88, 165, 143, 198...
%e 13, 39, 52, 91, 78, 156, 104, 195, 169, 234...
%e 17, 51, 68, 119, 102, 204, 136, 255, 221, 306...
%e 19, 57, 76, 133, 114, 228, 152, 285, 247, 342...
%e 23, 69, 92, 161, 138, 276, 184, 345, 299, 414...
%e ...
%t Table[If[# == 1, 1, Prime[# - 1]] DivisorSigma[1, k] &@(n - k + 1), {n, 12}, {k, n}] // Flatten (* _Michael De Vlieger_, Apr 28 2016 *)
%Y Rows 1-3: A000203, A074400, A272027.
%Y Columns 1-2: A008578, A112773.
%Y The diagonal 2, 9, 20... is A272211, the main diagonal of A272214.
%Y Cf. A272173.
%K nonn,tabl
%O 1,2
%A _Omar E. Pol_, Apr 28 2016