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A319334
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Nonprime Heinz numbers of integer partitions whose sum is equal to their LCM.
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1
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30, 198, 264, 273, 364, 490, 525, 630, 700, 840, 918, 1120, 1224, 1495, 1632, 1794, 2392, 2420, 2750, 3105, 3450, 3726, 4140, 4263, 4400, 4466, 4921, 4968, 5481, 5520, 5684, 6327, 6624, 7030, 7040, 7308, 8436, 8832, 9744, 11248, 12992, 14079, 14450, 14993
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OFFSET
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1,1
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COMMENTS
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The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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Table of n, a(n) for n=1..44.
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EXAMPLE
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The sequence of all non-singleton integer partitions whose sum is equal to their LCM begins: (321), (5221), (52111), (642), (6411), (4431), (4332), (43221), (43311), (432111), (72221), (4311111), (722111), (963), (7211111), (9621).
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[2, 1000], And[!PrimeQ[#], LCM@@primeMS[#]==Total[primeMS[#]]]&]
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CROSSREFS
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Cf. A067538, A074761, A143773, A290103, A305566, A316429, A316431, A316432, A316433, A317624, A319315, A319333.
Sequence in context: A249467 A309924 A120339 * A064247 A125340 A126498
Adjacent sequences: A319331 A319332 A319333 * A319335 A319336 A319337
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Sep 17 2018
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STATUS
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approved
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