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A327476
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Heinz numbers of integer partitions whose mean A326567/A326568 is not a part.
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52
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1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 106
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OFFSET
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1,2
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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:
1: {}
6: {1,2}
10: {1,3}
12: {1,1,2}
14: {1,4}
15: {2,3}
18: {1,2,2}
20: {1,1,3}
21: {2,4}
22: {1,5}
24: {1,1,1,2}
26: {1,6}
28: {1,1,4}
33: {2,5}
34: {1,7}
35: {3,4}
36: {1,1,2,2}
38: {1,8}
39: {2,6}
40: {1,1,1,3}
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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[100], !MemberQ[primeMS[#], Mean[primeMS[#]]]&]
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CROSSREFS
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The enumeration of these partitions by sum is given by A327472.
Subsets whose mean is not an element are A327471.
Cf. A056239, A067538, A112798, A114639, A237984, A240851, A316413, A324756, A324758, A326567/A326568, A327477.
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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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