A316893 Number of aperiodic integer partitions of n into relatively prime parts whose reciprocal sum is 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

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