A093313 Number of permutations s_1,s_2,...,s_n of 1,2,...,n with s_1 = 2 and such that for all j=1,2,...,n, s_j divides Sum_{i=1..j} s_i.

0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 1, 11, 9, 15, 14, 14, 23

Offset: 1

Author

Matthijs Coster, Apr 26 2004; revised Aug 05 2005

Keywords

• nonn
• more

Comments

An easy calculation turns out that the beginning elements are always: 2,1,3,6,(then either 4 or 12),...

The total number of permutations with this property is given in A067957.

Examples

			There is a unique permutation of the numbers 1..38, starting with 2, namely:
2 1 3 6 12 24 8 28 21 35 14 22 4 20 25 5 23 11 33 27 9 37 10 19 7 29 15 30 16 31 17 32 36 34 38 18 26 13
with corresponding sums
2 3 6 12 24 48 56 84 105 140 154 176 180 200 225 230 253 264 297 324 333 370 380 399 406 435 450 480 496 527 544 576 612 646 684 702 728 741.
		

Links

• Matthijs Coster, Sequences
• Matthijs Coster, Problem 2001/3-A of the Universitaire Wiskunde Competitie, Nieuw Arch. Wisk. 5/3 (2002), 92-94.

Crossrefs

Cf. A067957, A093314, A093315.