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A316897 Number of integer partitions of n into relatively prime parts whose reciprocal sum is 1. 0
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 3, 1, 2, 1, 1, 1, 2, 1, 5, 3, 1, 1, 5, 2, 9, 3, 3, 3, 4, 2, 6, 6, 3, 4, 9, 5, 10, 5, 10, 9, 15, 10, 21, 12, 14, 16, 18, 9, 30, 18, 17, 17, 28, 16, 29, 26, 26, 30, 28, 33, 48, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,22

COMMENTS

The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.

LINKS

Table of n, a(n) for n=1..80.

Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums

EXAMPLE

The a(43) = 9 partitions:

(24,8,4,4,3)

(21,7,7,6,2)

(20,12,5,3,3)

(20,8,8,5,2)

(15,15,6,5,2)

(15,12,10,4,2)

(14,7,7,7,4,4)

(12,8,8,6,6,3)

(10,10,10,5,4,4).

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], And[GCD@@#==1, Sum[1/m, {m, #}]==1]&]], {n, 30}]

CROSSREFS

Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316888-A316904.

Sequence in context: A309395 A260943 A316893 * A151756 A112053 A089798

Adjacent sequences:  A316894 A316895 A316896 * A316898 A316899 A316900

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 16 2018

EXTENSIONS

a(71)-a(80) from Giovanni Resta, Jul 16 2018

STATUS

approved

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Last modified April 13 15:23 EDT 2021. Contains 342936 sequences. (Running on oeis4.)