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A319157 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. 2
2, 3, 9, 441, 11865091329, 284788749974468882877009302517495014698593896453070311184452244729 (list; graph; refs; listen; history; text; internal format)



The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

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.


Table of n, a(n) for n=1..6.


Function[m, Times@@Prime/@m]/@NestList[Join@@Table[Table[2i, {Reverse[#][[i]]}], {i, Length[#]}]&, {1}, 4]


Cf. A001462, A001597, A056239, A072774, A181819, A182850, A182857, A304455, A304464, A317246, A317257, A319149, A319151.

Sequence in context: A132537 A251543 A248236 * A153702 A280941 A130110

Adjacent sequences:  A319154 A319155 A319156 * A319158 A319159 A319160




Gus Wiseman, Sep 12 2018



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Last modified December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)