A316901 Heinz numbers of integer partitions into relatively prime parts whose reciprocal sum is the reciprocal of an integer.

2, 195, 3185, 5467, 6475, 6815, 8455, 10527, 15385, 16401, 17719, 20445, 20535, 21045, 25365, 28897, 40001, 46155, 49841, 50431, 54677, 92449, 101543, 113849, 123469, 137731, 156883, 164255, 171941, 185803, 218855, 228085, 230347, 261457, 267883, 274261

Offset

1,1

Comments

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

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Links

Table of n, a(n) for n=1..36.

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

Example

5467 is the Heinz number of (20,5,4) and 1/20 + 1/5 + 1/4 = 1/2, so 5467 belongs to the sequence.
The sequence of partitions whose Heinz numbers belong to this sequence begins: (1), (6,3,2), (6,4,4,3), (20,5,4), (12,4,3,3), (15,10,3), (24,8,3), (10,5,5,2)

Mathematica

Select[Range[2, 100000], And[GCD@@PrimePi/@FactorInteger[#][[All, 1]]==1, IntegerQ[1/Sum[m[[2]]/PrimePi[m[[1]]], {m, FactorInteger[#]}]]]&]

Crossrefs

Cf. A000837, A002966, A051908, A058360, A100953, A289509, A296150, A316854, A316855, A316856, A316857, A316888-A316904.

Sequence in context: A139949 A229017 A103429 * A316888 A316890 A143659

Adjacent sequences: A316898 A316899 A316900 * A316902 A316903 A316904

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Status

approved