A319327 Heinz numbers of integer partitions such that every distinct submultiset has a different LCM.

1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 51, 53, 55, 59, 61, 67, 69, 71, 73, 77, 79, 83, 85, 89, 91, 93, 95, 97, 101, 103, 107, 109, 113, 119, 123, 127, 131, 137, 139, 141, 143, 145, 149, 151, 155, 157, 161, 163, 165, 167, 173

Offset: 1

Author

Gus Wiseman, Sep 17 2018

Keywords

• nonn

Comments

Note that such a Heinz number is necessarily squarefree, as such a partition is necessarily strict.

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

First differs from A304713 (Heinz numbers of pairwise indivisible partitions) at A304713(642) = 2093, which is absent from this sequence because its prime indices are {4,6,9} and LCM(4,9) = LCM(4,6,9) = 36.

Examples

			The sequence of partitions whose Heinz numbers are in the sequence begins: (), (1), (2), (3), (4), (5), (6), (3,2), (7), (8), (9), (10), (11), (5,2), (4,3), (12), (13), (14), (15), (7,2).
		

Crossrefs

Cf. A056239, A108917, A122768, A275972, A299702, A301899, A301900, A304713, A316313, A319315, A319319, A319320.

Programs

Mathematica

primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],UnsameQ@@LCM@@@Union[Subsets[primeMS[#]]]&]