1,5

The array can be constructed by beginning with A007318 (Pascal's triangle) placing each diagonal on a prime row. The other rows are filled in by mapping the prime factorization of the row number to the known sequences on the prime rows and multiplying term by term.

Row six begins 1 6 18 40 75 126 ... because rows two and three are

1 2 3 4 5 6 ...

1 3 6 10 15 21 ...

The array begins

1 1 1 1 1 1 1 1 1

1 2 3 4 5 6 7 8 9

1 3 6 10 15 21 28 36 45

1 4 9 16 25 36 49 64 81

1 4 10 20 35 56 84 120 165

1 6 18 40 75 126 196 288 405

1 5 15 35 70 126 210 330 495

1 8 27 64 125 216 343 512 729

1 9 36 100 225 441 784 1296 2025

1 8 30 80 175 336 588 960 1485

1 6 21 56 126 252 462 792 1287

1 12 54 160 375 756 1372 2304 3645

1 7 28 84 210 462 924 1716 3003

1 10 45 140 350 756 1470 2640 4455

1 12 60 200 525 1176 2352 4320 7425

1 16 81 256 625 1296 2401 4096 6561

1 8 36 120 330 792 1716 3432 6435

1 18 108 400 1125 2646 5488 10368 18225

1 9 45 165 495 1287 3003 6435 12870

1 16 90 320 875 2016 4116 7680 13365

1 15 90 350 1050 2646 5880 11880 22275

1 12 63 224 630 1512 3234 6336 11583

1 10 55 220 715 2002 5005 11440 24310

1 24 162 640 1875 4536 9604 18432 32805

1 16 100 400 1225 3136 7056 14400 27225

1 14 84 336 1050 2772 6468 13728 27027

1 27 216 1000 3375 9261 21952 46656 91125

1 20 135 560 1750 4536 10290 21120 40095

Cf. A000040 A007318.

Cf. A064553 (second diagonal), A080688 (second diagonal resorted).

Sequence in context: A067049 A090641 A055216 this_sequence A107065 A008975 A140280

Adjacent sequences: A128626 A128627 A128628 this_sequence A128630 A128631 A128632

easy,nonn,tabl

Alford Arnold (Alford1940(AT)aol.com), Mar 29 2007