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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.
3
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
1,2
FORMULA
T(n,k) = A008578(n)*A000203(k), n>=1, k>=1.
T(n,k) = A272214(n-1,k), n>=2.
EXAMPLE
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...
...
MATHEMATICA
Table[If[# == 1, 1, Prime[# - 1]] DivisorSigma[1, k] &@(n - k + 1), {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Apr 28 2016 *)
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.
Sequence in context: A021432 A274824 A141729 * A238305 A337660 A049990
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Apr 28 2016
STATUS
approved