A301764 Number of ways to choose a constant rooted partition of each part in a constant rooted partition of n such that the flattened sequence is also constant.

1, 1, 2, 3, 4, 4, 6, 5, 6, 7, 8, 5, 10, 7, 8, 10, 10, 6, 12, 7, 12, 13, 10, 5, 14, 12, 11, 11, 14, 7, 18, 9, 12, 13, 11, 12, 20, 10, 10, 13, 18, 9, 20, 9, 14, 20, 12, 5, 20, 15, 19, 14, 17, 7, 18, 16, 20, 17, 12, 5, 26, 13, 12, 21, 18, 17, 24, 9, 15, 13, 22, 9

Offset

1,3

Comments

A rooted partition of n is an integer partition of n - 1.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Example

The a(11) = 8 rooted twice-partitions: (9), (333), (111111111), (4)(4), (22)(22), (1111)(1111), (1)(1)(1)(1)(1), ()()()()()()()()()().

Mathematica

Table[If[n===1, 1, DivisorSum[n-1, If[#===1, 1, DivisorSigma[0, #-1]]&]], {n, 100}]

Prog

(PARI) a(n)=if(n==1, 1, sumdiv(n-1, d, if(d==1, 1, numdiv(d-1)))) \\ Andrew Howroyd, Aug 26 2018

Crossrefs

Cf. A002865, A007425, A063834, A093637, A127524, A295931, A300383, A301422, A301462, A301467, A301480, A301706.

Sequence in context: A365851 A091860 A333995 * A181833 A202650 A228286

Adjacent sequences: A301761 A301762 A301763 * A301765 A301766 A301767

Keyword

nonn

Author

Gus Wiseman, Mar 26 2018

Status

approved