A094098 -id:A094098 - cp's OEIS frontend

A067957 Number of divisor chains of length n: permutations s_1,s_2,...,s_n of 1,2,...,n such that for all j=1,2,...,n, s_j divides Sum_{i=1..j} s_i.

1, 1, 1, 2, 2, 4, 5, 7, 7, 24, 22, 29, 39, 67, 55, 386, 235, 312, 347, 451, 1319, 5320, 3220, 4489, 20237, 36580, 52875, 197103, 216562, 289478, 567396, 659647, 1111153, 3131774, 2200426, 29523302, 34214028, 48161995, 32616148, 242860900, 293579041, 363415618

Offset: 0

Floor van Lamoen, Mar 06 2002

nonn

Apparently this sequence originated in a problem composed by Matthijs Coster in 2002.

Let M = floor(n/2), then the following permutations always work: for n even: M+1, 1, M+2, 2, ..., n-1, M-1, n, M; for n odd: M+1, 1, M+2, 2, ..., M-1, n-1, M, n. - Daniel Asimov, May 04 2004

			Examples of divisor chains of lengths 1 through 9:
  1
  2 1
  3 1 2
  4 2 3 1
  5 1 2 4 3
  6 2 4 3 5 1
  7 1 2 5 3 6 4
  8 2 5 3 6 4 7 1
  8 4 3 5 1 7 2 6 9
The five divisor chains of length 6 are:
  4 1 5 2 6 3
  4 2 6 3 5 1
  5 1 2 4 6 3
  5 1 6 4 2 3
  6 2 4 3 5 1. - Eugene McDonnell, May 21 2004

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

Cf. A093313, A093314, A093315, A094097, A094098, A094099.

a(31)-a(35) from Jud McCranie, May 06 2004
a(0)=1 prepended by Alois P. Heinz, Aug 26 2017
a(36)-a(41) from Zhao Hui Du, May 12 2024

A094097 Number of divisor chains of length n which begin with n ("anchored" divisor chains).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 5, 4, 3, 2, 8, 4, 6, 47, 44, 6, 37, 6, 166, 462, 232, 372, 2130, 1589, 9093, 20896, 20314, 4118, 32367, 12815, 167796, 130528, 59173, 1942045, 2607312, 163775, 1297794, 18340336, 22304602, 5065878, 21005347, 3607762, 129164605

Offset: 1

N. J. A. Sloane, following a suggestion of R. K. Guy, May 04 2004

nonn

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 of divisor chains of lengths 1 through 8:
1
2 1
3 1 2
4 2 3 1
5 1 2 4 3
6 2 4 3 5 1
7 1 2 5 3 6 4
8 2 5 3 6 4 7 1

Cf. A067957, A094098, A094099.

Right diagonal of A093323.

a(1)-a(9) from R. K. Guy and Paul Vaderlind
a(10)-a(19) from Ed Clark, Jr. and Chuck Seggelin
a(20)-a(28) from Christopher Landauer, May 04 2004
a(29)-a(37) from Joseph Myers, May 04 2004
a(38) from Jud McCranie, May 07 2004
a(39)-a(44) from Joseph Myers, May 21 2004

A094099 Number of divisor chains of length 2n+1 which are both cyclic and anchored.

Original entry on oeis.org

1, 1, 1, 1, 4, 2, 4, 47, 6, 6, 462, 372, 1589, 20896, 4118, 12815, 130528, 1942045, 163775, 18340336, 5065878, 3607762

Offset: 0

Christopher Landauer, May 04 2004

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.

Cf. A067957, A094097, A094098, A094099.

a(n) = A094097(2n+1). - Martin Fuller, Jul 18 2025

a(14)-a(21) from A094097 by Martin Fuller, Jul 18 2025

cp's OEIS Frontend

A067957 Number of divisor chains of length n: permutations s_1,s_2,...,s_n of 1,2,...,n such that for all j=1,2,...,n, s_j divides Sum_{i=1..j} s_i.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A094097 Number of divisor chains of length n which begin with n ("anchored" divisor chains).

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A094099 Number of divisor chains of length 2n+1 which are both cyclic and anchored.

Views

Author

Keywords

Comments

Crossrefs

Formula

Extensions