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A272214 Square array read by antidiagonals upwards in which T(n,k) is the product of the n-th prime and the sum of the divisors of k, n>=1, k>=1. 5
2, 3, 6, 5, 9, 8, 7, 15, 12, 14, 11, 21, 20, 21, 12, 13, 33, 28, 35, 18, 24, 17, 39, 44, 49, 30, 36, 16, 19, 51, 52, 77, 42, 60, 24, 30, 23, 57, 68, 91, 66, 84, 40, 45, 26, 29, 69, 76, 119, 78, 132, 56, 75, 39, 36, 31, 87, 92, 133, 102, 156, 88, 105, 65, 54, 24, 37, 93, 116, 161, 114, 204, 104, 165, 91, 90, 36, 56 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..8128

FORMULA

T(n,k) = prime(n)*sigma(k) = A000040(n)*A000203(k), n>=1, k>=1.

T(n,k) = A272400(n+1,k).

EXAMPLE

The corner of the square array begins:

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...

29, 87, 116, 203, 174, 348, 232, 435, 377, 522...

...

MATHEMATICA

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

CROSSREFS

Rows 1-2: A074400, A272027.

Columns 1-5: A000040, A001748, A001749, A138636, A272470.

Main diagonal gives A272211.

Cf. A000203, A272173, A272400.

Sequence in context: A328638 A327420 A119790 * A319785 A080029 A091239

Adjacent sequences:  A272211 A272212 A272213 * A272215 A272216 A272217

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Apr 28 2016

STATUS

approved

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Last modified July 4 15:25 EDT 2020. Contains 335448 sequences. (Running on oeis4.)