A360070 Numbers for which there exists an integer partition such that the parts have the same mean as the multiplicities.

1, 4, 8, 9, 12, 16, 18, 20, 25, 27, 32, 36, 45, 48, 49, 50, 54, 63, 64, 72, 75, 80, 81, 90, 96, 98, 99, 100, 108, 112, 117, 121, 125, 128, 144, 147, 150, 160, 162, 169, 175, 176, 180, 192, 196, 200, 208, 216, 224, 225, 240, 242, 243, 245, 250, 252, 256, 272

Offset

1,2

Comments

Conjecture: No term > 1 is squarefree.

Links

Table of n, a(n) for n=1..58.

Example

A partition of 20 with the same mean as its multiplicities is (5,4,3,2,1,1,1,1,1,1), so 20 is in the sequence.

Mathematica

Select[Range[30], Select[IntegerPartitions[#], Mean[#]==Mean[Length/@Split[#]]&]!={}&]

Crossrefs

Positions of positive terms in A360068, ranked by A359903.

A000041 counts partitions, strict A000009.

A058398 counts partitions by mean, see also A008284, A327482.

A088529/A088530 gives mean of prime signature (A124010).

A326567/A326568 gives mean of prime indices (A112798).

Cf. A005117, A067340, A067538, A240219, A316313, A349156, A359904, A359905, A360069.

Sequence in context: A034043 A278517 A053443 * A048098 A322109 A122145

Adjacent sequences: A360067 A360068 A360069 * A360071 A360072 A360073

Keyword

nonn

Author

Gus Wiseman, Jan 27 2023

Extensions

a(22)-a(58) from Alois P. Heinz, Jan 29 2023

Status

approved