A343939 Number of n-chains of divisors of n.

1, 3, 4, 15, 6, 49, 8, 165, 55, 121, 12, 1183, 14, 225, 256, 4845, 18, 3610, 20, 4851, 484, 529, 24, 73125, 351, 729, 4060, 12615, 30, 29791, 32, 435897, 1156, 1225, 1296, 494209, 38, 1521, 1600, 505981, 42, 79507, 44, 46575, 49726, 2209, 48

Offset

1,2

Links

Table of n, a(n) for n=1..47.

Example

The a(1) = 1 through a(5) = 6 chains:
  (1)  (1/1)  (1/1/1)  (1/1/1/1)  (1/1/1/1/1)
       (2/1)  (3/1/1)  (2/1/1/1)  (5/1/1/1/1)
       (2/2)  (3/3/1)  (2/2/1/1)  (5/5/1/1/1)
              (3/3/3)  (2/2/2/1)  (5/5/5/1/1)
                       (2/2/2/2)  (5/5/5/5/1)
                       (4/1/1/1)  (5/5/5/5/5)
                       (4/2/1/1)
                       (4/2/2/1)
                       (4/2/2/2)
                       (4/4/1/1)
                       (4/4/2/1)
                       (4/4/2/2)
                       (4/4/4/1)
                       (4/4/4/2)
                       (4/4/4/4)

Mathematica

Table[Length[Select[Tuples[Divisors[n], n], OrderedQ[#]&&And@@Divisible@@@Reverse/@Partition[#, 2, 1]&]], {n, 10}]

Crossrefs

Diagonal n = k - 1 of the array A077592.

Chains of length n - 1 are counted by A163767.

Diagonal n = k of the array A334997.

The version counting all multisets of divisors (not just chains) is A343935.

A000005(n) counts divisors of n.

A067824(n) counts strict chains of divisors starting with n.

A074206(n) counts strict chains of divisors from n to 1.

A146291(n,k) counts divisors of n with k prime factors (with multiplicity).

A251683(n,k-1) counts strict k-chains of divisors from n to 1.

A253249(n) counts nonempty chains of divisors of n.

A334996(n,k) counts strict k-chains of divisors from n to 1.

A337255(n,k) counts strict k-chains of divisors starting with n.

A343658(n,k) counts k-multisets of divisors of n.

A343662(n,k) counts strict k-chains of divisors of n (row sums: A337256).

Cf. A062319, A066959, A143773, A176029, A327527, A343656.

Sequence in context: A365349 A258468 A327275 * A157351 A071167 A194924

Adjacent sequences: A343936 A343937 A343938 * A343940 A343941 A343942

Keyword

nonn

Author

Gus Wiseman, May 05 2021

Status

approved