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A319328 Heinz numbers of integer partitions such that not every distinct submultiset has a different GCD but every distinct submultiset has a different LCM. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A323379

Adjacent sequences:  A319325 A319326 A319327 * A319329 A319330 A319331

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 17 2018

STATUS

approved

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Last modified November 30 03:48 EST 2021. Contains 349417 sequences. (Running on oeis4.)