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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
2, 1495, 179417, 231133, 727531 (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).
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
Sequence in context: A172234 A339543 A023291 * A058423 A233906 A329775
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 17 2018
STATUS
approved

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Last modified July 21 20:59 EDT 2024. Contains 374475 sequences. (Running on oeis4.)