

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.


4



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
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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 twicepartitions: (9), (333), (111111111), (4)(4), (22)(22), (1111)(1111), (1)(1)(1)(1)(1), ()()()()()()()()()().


MATHEMATICA

Table[If[n===1, 1, DivisorSum[n1, If[#===1, 1, DivisorSigma[0, #1]]&]], {n, 100}]


PROG

(PARI) a(n)=if(n==1, 1, sumdiv(n1, d, if(d==1, 1, numdiv(d1)))) \\ Andrew Howroyd, Aug 26 2018


CROSSREFS

Cf. A002865, A007425, A063834, A093637, A127524, A295931, A300383, A301422, A301462, A301467, A301480, A301706.
Sequence in context: A298933 A091860 A333995 * A181833 A202650 A228286
Adjacent sequences: A301761 A301762 A301763 * A301765 A301766 A301767


KEYWORD

nonn


AUTHOR

Gus Wiseman, Mar 26 2018


STATUS

approved



