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A338909
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Numbers of the form prime(x) * prime(y) where x and y have a common divisor > 1.
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7
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9, 21, 25, 39, 49, 57, 65, 87, 91, 111, 115, 121, 129, 133, 159, 169, 183, 185, 203, 213, 235, 237, 247, 259, 267, 289, 299, 301, 303, 305, 319, 321, 339, 361, 365, 371, 377, 393, 417, 427, 445, 453, 481, 489, 497, 515, 517, 519, 529, 543, 551, 553, 559, 565
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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The sequence of terms together with their prime indices begins:
9: {2,2} 169: {6,6} 319: {5,10}
21: {2,4} 183: {2,18} 321: {2,28}
25: {3,3} 185: {3,12} 339: {2,30}
39: {2,6} 203: {4,10} 361: {8,8}
49: {4,4} 213: {2,20} 365: {3,21}
57: {2,8} 235: {3,15} 371: {4,16}
65: {3,6} 237: {2,22} 377: {6,10}
87: {2,10} 247: {6,8} 393: {2,32}
91: {4,6} 259: {4,12} 417: {2,34}
111: {2,12} 267: {2,24} 427: {4,18}
115: {3,9} 289: {7,7} 445: {3,24}
121: {5,5} 299: {6,9} 453: {2,36}
129: {2,14} 301: {4,14} 481: {6,12}
133: {4,8} 303: {2,26} 489: {2,38}
159: {2,16} 305: {3,18} 497: {4,20}
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MATHEMATICA
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Select[Range[100], PrimeOmega[#]==2&&GCD@@PrimePi/@First/@FactorInteger[#]>1&]
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CROSSREFS
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A082023 counts partitions with these as Heinz numbers, complement A023022.
A001221 counts distinct prime indices.
A004526 counts 2-part partitions, with strict case A140106 (shifted left).
A318990 lists semiprimes with divisible indices.
A320655 counts factorizations into semiprimes.
A338910 lists semiprimes with odd indices.
A338911 lists semiprimes with even indices.
Cf. A005117, A037143, A055684, A056239, A065516, A112798, A115392, A128301, A289182, A338900, A338904.
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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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