

A319329


Heinz numbers of integer partitions whose length is equal to the GCD of the parts and whose sum is equal to the LCM of the parts.


1




OFFSET

1,1


COMMENTS

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


LINKS



EXAMPLE

The sequence of partitions whose length is equal to their GCD and whose sum is equal to their LCM begins: (1), (9,6,3), (20,8,8,4), (24,16,4,4), (16,16,12,4).


MATHEMATICA

Select[Range[2, 10000], With[{m=If[#==1, {}, Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]}, And[LCM@@m==Total[m], GCD@@m==Length[m]]]&]


CROSSREFS

Cf. A056239, A067538, A074761, A143773, A289508, A289509, A290103, A290104, A316430, A316431, A316432, A319328, A319330, A319333.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



