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A303282
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Numbers whose prime indices have no common divisor other than 1 but are not pairwise coprime.
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12
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18, 36, 42, 45, 50, 54, 72, 75, 78, 84, 90, 98, 99, 100, 105, 108, 114, 126, 130, 135, 144, 150, 153, 156, 162, 168, 174, 175, 180, 182, 195, 196, 198, 200, 207, 210, 216, 222, 225, 228, 230, 231, 234, 242, 245, 250, 252, 258, 260, 266, 270, 275, 279, 285, 288
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OFFSET
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1,1
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. Two or more numbers are coprime if no pair of them has a common divisor other than 1.
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 integer partitions whose Heinz numbers belong to this sequence begins (221), (2211), (421), (322), (331), (2221), (22111), (332), (621), (4211), (3221), (441), (522), (3311), (432), (22211).
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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[400], !CoprimeQ@@primeMS[#]&&GCD@@primeMS[#]===1&]
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CROSSREFS
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Cf. A000837, A001222, A018783, A051424, A056239, A078374, A168532, A289508, A289509, A296150, A298748, A300486, A302569, A302696, A302796, A303138, A303139, A303140, A303283.
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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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