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

1,1

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}.

Links

Table of n, a(n) for n=1..45.

Example

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).

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[#]]]]]&]

Crossrefs

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

Sequence in context: A259283 A319502 A270175 * A301970 A176877 A356095

Adjacent sequences: A319325 A319326 A319327 * A319329 A319330 A319331

Keyword

nonn

Author

Gus Wiseman, Sep 17 2018

Status

approved