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A316893 Number of aperiodic integer partitions of n into relatively prime parts whose reciprocal sum is 1. 1
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, 4, 10, 8, 15, 10, 21, 12, 14, 16, 18, 9, 30, 18, 17, 16, 28, 16, 29, 25, 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.

A partition is aperiodic if its multiplicities are relatively prime.

LINKS

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

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

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A332007 A309395 A260943 * A316897 A151756 A112053

Adjacent sequences:  A316890 A316891 A316892 * A316894 A316895 A316896

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 June 17 05:45 EDT 2021. Contains 345080 sequences. (Running on oeis4.)