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A327776
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Heinz numbers of integer partitions whose LCM is less than their sum.
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4
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4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 32, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 68, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 94, 96, 98, 100, 104, 106, 108, 111, 112
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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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EXAMPLE
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The sequence of terms together with their prime indices begins:
4: {1,1}
6: {1,2}
8: {1,1,1}
9: {2,2}
10: {1,3}
12: {1,1,2}
14: {1,4}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
21: {2,4}
22: {1,5}
24: {1,1,1,2}
25: {3,3}
26: {1,6}
27: {2,2,2}
28: {1,1,4}
32: {1,1,1,1,1}
34: {1,7}
36: {1,1,2,2}
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MAPLE
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q:= n-> (l-> is(ilcm(l[])<add(j, j=l)))(map(i->
numtheory[pi](i[1])$i[2], ifactors(n)[2])):
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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, 100], LCM@@primeMS[#]<Total[primeMS[#]]&]
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CROSSREFS
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The enumeration of these partitions by sum is A327781.
Heinz numbers of partitions whose LCM is twice their sum are A327775.
Heinz numbers of partitions whose LCM is a multiple their sum are A327783.
Heinz numbers of partitions whose LCM is greater than their sum are A327784.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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