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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.
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%I #8 Aug 27 2018 01:52:43

%S 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,

%T 14,7,18,9,12,13,11,12,20,10,10,13,18,9,20,9,14,20,12,5,20,15,19,14,

%U 17,7,18,16,20,17,12,5,26,13,12,21,18,17,24,9,15,13,22,9

%N 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.

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

%H Andrew Howroyd, <a href="/A301764/b301764.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%o (PARI) a(n)=if(n==1, 1, sumdiv(n-1, d, if(d==1, 1, numdiv(d-1)))) \\ _Andrew Howroyd_, Aug 26 2018

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

%K nonn

%O 1,3

%A _Gus Wiseman_, Mar 26 2018