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.

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, 8, 17, 39, 44, 49, 30, 36, 16, 15, 19, 51, 52, 77, 42, 60, 24, 30, 13, 23, 57, 68, 91, 66, 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

Offset: 1

Author

Omar E. Pol, Apr 28 2016

Keywords

• nonn
• tabl

Examples

			The corner of the square array begins:
1,   3,   4,   7,   6,  12,   8,  15,  13,  18...
2,   6,   8,  14,  12,  24,  16,  30,  26,  36...
3,   9,  12,  21,  18,  36,  24,  45,  39,  54...
5,  15,  20,  35,  30,  60,  40,  75,  65,  90...
7,  21,  28,  49,  42,  84,  56, 105,  91, 126...
11, 33,  44,  77,  66, 132,  88, 165, 143, 198...
13, 39,  52,  91,  78, 156, 104, 195, 169, 234...
17, 51,  68, 119, 102, 204, 136, 255, 221, 306...
19, 57,  76, 133, 114, 228, 152, 285, 247, 342...
23, 69,  92, 161, 138, 276, 184, 345, 299, 414...
...
		

Crossrefs

Rows 1-3: A000203, A074400, A272027.

Columns 1-2: A008578, A112773.

The diagonal 2, 9, 20... is A272211, the main diagonal of A272214.

Cf. A272173.

Programs

Mathematica

Table[If[# == 1, 1, Prime[# - 1]] DivisorSigma[1, k] &@(n - k + 1), {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Apr 28 2016 *)

Formula

T(n,k) = A008578(n)*A000203(k), n>=1, k>=1.

T(n,k) = A272214(n-1,k), n>=2.