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%I #9 Nov 17 2018 20:46:54
%S 2,3,9,441,11865091329,
%T 284788749974468882877009302517495014698593896453070311184452244729
%N Smallest Heinz number of a superperiodic integer partition requiring n steps in the reduction to a multiset of size 1 obtained by repeatedly taking the multiset of multiplicities.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C An integer partition is superperiodic if either it consists of a single part equal to 1 or its parts have a common divisor > 1 and its multiset of multiplicities is itself superperiodic. For example, (8,8,6,6,4,4,4,4,2,2,2,2) has multiplicities (4,4,2,2) with multiplicities (2,2) with multiplicities (2) with multiplicities (1). The first four of these partitions are periodic and the last is (1), so (8,8,6,6,4,4,4,4,2,2,2,2) is superperiodic.
%t Function[m,Times@@Prime/@m]/@NestList[Join@@Table[Table[2i,{Reverse[#][[i]]}],{i,Length[#]}]&,{1},4]
%Y Cf. A001462, A001597, A056239, A072774, A181819, A182850, A182857, A304455, A304464, A317246, A317257, A319149, A319151.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 12 2018
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