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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 Table of n, a(n) for n=1..5. 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. Sequence in context: A172234 A339543 A023291 * A058423 A233906 A329775 Adjacent sequences: A319326 A319327 A319328 * A319330 A319331 A319332 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.)