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, 3, 9, 441, 11865091329, 284788749974468882877009302517495014698593896453070311184452244729

Offset

1,1

Comments

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.

Links

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

Mathematica

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

Crossrefs

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

Sequence in context: A332203 A350777 A248236 * A153702 A280941 A347122

Adjacent sequences: A319154 A319155 A319156 * A319158 A319159 A319160

Keyword

nonn

Author

Gus Wiseman, Sep 12 2018

Status

approved