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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
OFFSET
1,3
COMMENTS
A rooted partition of n is an integer partition of n - 1.
LINKS
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved