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

Author

Gus Wiseman, Jul 16 2018

Keywords

• nonn

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).

Examples

			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)
		

Links

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

Crossrefs

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

Programs

Mathematica

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