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

Author

Gus Wiseman, May 05 2021

Keywords

• nonn

Examples

			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)
		

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.

Programs

Mathematica

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