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A272400 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.

%I A272400 #19 Apr 29 2016 23:36:38
%S A272400 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 A272400 8,17,39,44,49,30,36,16,15,19,51,52,77,42,60,24,30,13,23,57,68,91,66,
%U A272400 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 A272400 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 A272400 T(n,k) = A008578(n)*A000203(k), n>=1, k>=1.
%F A272400 T(n,k) = A272214(n-1,k), n>=2.
%e A272400 The corner of the square array begins:
%e A272400 1,   3,   4,   7,   6,  12,   8,  15,  13,  18...
%e A272400 2,   6,   8,  14,  12,  24,  16,  30,  26,  36...
%e A272400 3,   9,  12,  21,  18,  36,  24,  45,  39,  54...
%e A272400 5,  15,  20,  35,  30,  60,  40,  75,  65,  90...
%e A272400 7,  21,  28,  49,  42,  84,  56, 105,  91, 126...
%e A272400 11, 33,  44,  77,  66, 132,  88, 165, 143, 198...
%e A272400 13, 39,  52,  91,  78, 156, 104, 195, 169, 234...
%e A272400 17, 51,  68, 119, 102, 204, 136, 255, 221, 306...
%e A272400 19, 57,  76, 133, 114, 228, 152, 285, 247, 342...
%e A272400 23, 69,  92, 161, 138, 276, 184, 345, 299, 414...
%e A272400 ...
%t A272400 Table[If[# == 1, 1, Prime[# - 1]] DivisorSigma[1, k] &@(n - k + 1), {n, 12}, {k, n}] // Flatten (* _Michael De Vlieger_, Apr 28 2016 *)
%Y A272400 Rows 1-3: A000203, A074400, A272027.
%Y A272400 Columns 1-2: A008578, A112773.
%Y A272400 The diagonal 2, 9, 20... is A272211, the main diagonal of A272214.
%Y A272400 Cf. A272173.
%K A272400 nonn,tabl
%O A272400 1,2
%A A272400 _Omar E. Pol_, Apr 28 2016