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A364348
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Numbers with two possibly equal divisors prime(a) and prime(b) such that prime(a+b) is also a divisor.
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16
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6, 12, 18, 21, 24, 30, 36, 42, 48, 54, 60, 63, 65, 66, 70, 72, 78, 84, 90, 96, 102, 105, 108, 114, 120, 126, 130, 132, 133, 138, 140, 144, 147, 150, 154, 156, 162, 165, 168, 174, 180, 186, 189, 192, 195, 198, 204, 210, 216, 222, 228, 231, 234, 240, 246, 252
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OFFSET
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1,1
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COMMENTS
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Or numbers with a 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 A363225.
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LINKS
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EXAMPLE
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We have 6 because prime(1) and prime(1) are both divisors of 6, and prime(1+1) is also.
The terms together with their prime indices begin:
6: {1,2}
12: {1,1,2}
18: {1,2,2}
21: {2,4}
24: {1,1,1,2}
30: {1,2,3}
36: {1,1,2,2}
42: {1,2,4}
48: {1,1,1,1,2}
54: {1,2,2,2}
60: {1,1,2,3}
63: {2,2,4}
65: {3,6}
66: {1,2,5}
70: {1,3,4}
72: {1,1,1,2,2}
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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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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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