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A319330 Number of integer partitions of n whose length is equal to the GCD of the parts and whose sum is equal to the LCM of the parts. 1
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 1, 0, 3, 0, 0, 0, 0, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,48

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

A list of all such partitions begins (1), (9,6,3), (20,8,8,4), (24,16,4,4), (16,16,12,4), (16,12,12,8), (25,10,5,5,5), (20,15,15,5,5), (20,15,10,10,5).

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], And[LCM@@#==Total[#], GCD@@#==Length[#]]&]], {n, 30}]

CROSSREFS

Cf. A067538, A074761, A143773, A316432, A319328, A319329, A319333.

Sequence in context: A180515 A009138 A175562 * A291204 A331414 A111025

Adjacent sequences:  A319327 A319328 A319329 * A319331 A319332 A319333

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 17 2018

EXTENSIONS

a(71)-a(105) from Alois P. Heinz, Sep 18 2018

STATUS

approved

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)