A319328 Heinz numbers of integer partitions such that not every distinct submultiset has a different GCD but every distinct submultiset has a different LCM.

165, 255, 385, 465, 561, 595, 615, 759, 885, 935, 1001, 1005, 1015, 1023, 1045, 1085, 1173, 1245, 1309, 1353, 1435, 1455, 1505, 1547, 1581, 1615, 1635, 1705, 1771, 1905, 1947, 2065, 2091, 2139, 2211, 2235, 2255, 2345, 2355, 2365, 2387, 2397, 2409, 2431, 2465

Offset: 1

Author

Gus Wiseman, Sep 17 2018

Keywords

• nonn

Comments

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

The first term of this sequence absent from A302696 (numbers whose prime indices are pairwise coprime) is 1001 with prime indices {4,5,6}.

Examples

			The sequence of partitions whose Heinz numbers belong to this sequence begins (5,3,2), (7,3,2), (5,4,3), (11,3,2), (7,5,2), (7,4,3), (13,3,2), (9,5,2), (17,3,2), (7,5,3).
		

Crossrefs

Cf. A056239, A275972, A299702, A301899, A301900, A319315, A319319, A319327.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[10000],UnsameQ@@primeMS[#]&&And[!UnsameQ@@GCD@@@Union[Rest[Subsets[primeMS[#]]]],UnsameQ@@LCM@@@Union[Rest[Subsets[primeMS[#]]]]]&]