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A319811 Number of totally aperiodic integer partitions of n. 1
1, 1, 2, 3, 6, 7, 14, 17, 27, 34, 55, 63, 99, 117, 162, 203, 286, 333, 469, 558, 737, 903, 1196, 1414, 1860, 2232, 2839, 3422, 4359, 5144, 6531, 7762, 9617, 11479, 14182, 16715, 20630, 24333, 29569, 34890, 42335, 49515, 59871, 70042, 83810, 98105, 117152 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

An integer partition is totally aperiodic iff either it is strict or it is aperiodic with totally aperiodic multiplicities.

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

The a(6) = 7 aperiodic integer partitions are: (6), (51), (42), (411), (321), (3111), (21111). The first aperiodic integer partition that is not totally aperiodic is (432211).

MATHEMATICA

totaperQ[m_]:=Or[UnsameQ@@m, And[GCD@@Length/@Split[Sort[m]]==1, totaperQ[Sort[Length/@Split[Sort[m]]]]]];

Table[Length[Select[IntegerPartitions[n], totaperQ]], {n, 30}]

CROSSREFS

Cf. A000837, A018783, A047966, A098859, A100953, A305563, A319149, A319160, A319162, A319163, A319164, A319810.

Sequence in context: A018606 A117087 A322367 * A000837 A200144 A056498

Adjacent sequences:  A319808 A319809 A319810 * A319812 A319813 A319814

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 28 2018

STATUS

approved

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Last modified October 18 05:22 EDT 2019. Contains 328146 sequences. (Running on oeis4.)