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A364347
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Numbers k > 0 such that if prime(a) and prime(b) both divide k, then prime(a+b) does not.
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22
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1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 64, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85
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OFFSET
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1,2
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COMMENTS
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Or numbers without any prime index equal to the sum of two others, allowing re-used parts.
Also Heinz numbers of a type of sum-free partitions counted by A364345.
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LINKS
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EXAMPLE
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We don't have 6 because prime(1), prime(1), and prime(1+1) are all divisors.
The terms together with their prime indices begin:
1: {}
2: {1}
3: {2}
4: {1,1}
5: {3}
7: {4}
8: {1,1,1}
9: {2,2}
10: {1,3}
11: {5}
13: {6}
14: {1,4}
15: {2,3}
16: {1,1,1,1}
17: {7}
19: {8}
20: {1,1,3}
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Intersection[prix[#], Total/@Tuples[prix[#], 2]]=={}&]
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CROSSREFS
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Subsets of this type are counted by A007865 (sum-free sets).
Partitions of this type are counted by A364345.
The squarefree case is counted by A364346.
The non-binary version is counted by A364350.
Without re-using parts we have complement A364462, counted by A237113.
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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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