A318716 Heinz numbers of strict integer partitions with relatively prime parts in which no two parts are relatively prime.

2, 17719, 40807, 43381, 50431, 74269, 83143, 101543, 105703, 116143, 121307, 123469, 139919, 140699, 142883, 171613, 181831, 185803, 191479, 203557, 205813, 211381, 213239, 215267, 219271, 246703, 249587, 249899, 279371, 286897, 289007, 296993, 300847, 303949

Offset

1,1

Comments

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..34.

Example

The sequence of strict integer partitions with Heinz numbers in the sequence begins: (1), (15,10,6), (21,14,6), (20,15,6), (15,12,10), (45,10,6), (18,15,10).

Mathematica

Select[Range[100000], With[{m=PrimePi/@FactorInteger[#][[All, 1]]}, And[SquareFreeQ[#], GCD@@m==1, And@@(GCD[##]>1&)@@@Select[Tuples[m, 2], Less@@#&]]]&]

Crossrefs

Cf. A078374, A289509, A302569, A302696, A302796, A302797, A303140, A303280, A303282, A303283, A305713, A318715, A318718, A318719.

Sequence in context: A242855 A367123 A214544 * A260252 A324437 A158344

Adjacent sequences: A318713 A318714 A318715 * A318717 A318718 A318719

Keyword

nonn

Author

Gus Wiseman, Sep 02 2018

Status

approved