A093323 Triangle read by rows giving number of divisor chains of length n beginning with k (1 <= k <= n).

1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 3, 1, 1, 0, 0, 0, 0, 1, 0, 1, 5, 0, 0, 0, 0, 1, 3, 4, 12, 4, 0, 0, 0, 0, 0, 4, 5, 7, 3, 3, 0, 0, 0, 0, 0, 4, 7, 9, 3, 4, 2, 0, 0, 0, 1, 0, 0, 2, 5, 4, 8, 11, 8, 0, 0, 0, 1, 0, 0, 2, 7, 11, 12, 19, 11, 4, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Eugene McDonnell (eemcd(AT)mac.com), May 11 2004

Keywords

• tabl
• nonn

Comments

A divisor chain of length n is an arrangement of 1..n such that each term is a divisor of the sum of the preceding terms.

Examples

			Triangle begins:
1
0 1
0 1 1
0 0 1 1
0 0 1 2 1
0 0 0 2 2 1
0 0 0 2 3 1 1
0 0 0 0 1 0 1 5
0 0 0 0 1 3 4 12 4
0 0 0 0 0 4 5 7 3 3
0 0 0 0 0 4 7 9 3 4 2
0 0 0 1 0 0 2 5 4 8 11 8
0 0 0 1 0 0 2 7 11 12 19 11 4
0 0 0 0 0 0 0 4 12 4 14 7 8 6
0 0 0 1 0 2 3 14 32 42 64 41 77 63 47
0 0 0 1 0 0 0 0 16 34 39 26 20 24 31 44
0 0 0 1 0 0 0 0 16 44 55 27 34 31 42 56 6
0 0 0 0 0 2 3 2 2 21 13 20 19 31 51 70 76 37
0 0 0 0 0 4 3 3 7 21 17 24 25 34 54 91 113 49 6
0 0 0 0 0 2 0 8 17 12 31 41 43 91 60 121 223 144 360 166
0 0 0 0 0 7 0 20 31 26 57 197 314 383 283 706 938 473 969 454 462
0 0 0 0 0 6 0 17 18 21 0 124 131 220 148 445 538 232 443 222 423 232
0 0 0 0 0 6 0 17 22 29 9 138 164 279 188 520 640 309 616 302 521 357 372
0 0 0 6 0 6 0 44 76 219 86 155 314 545 389 1354 1296 819 727 1246 1959 2619 6247 2130
0 0 0 8 0 11 7 60 112 257 102 273 323 1519 579 2388 2828 1600 2193 2535 3532 3955 9554 3155 1589
0 0 0 3 5 14 15 80 53 139 34 556 453 3063 1160 3194 1739 1756 2015 3648 5311 2903 7496 4084 6061 9093
		

Crossrefs

Cf. A094097 (right diagonal).