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A339002
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Numbers of the form prime(x) * prime(y) where x and y are distinct and have a common divisor > 1.
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6
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21, 39, 57, 65, 87, 91, 111, 115, 129, 133, 159, 183, 185, 203, 213, 235, 237, 247, 259, 267, 299, 301, 303, 305, 319, 321, 339, 365, 371, 377, 393, 417, 427, 445, 453, 481, 489, 497, 515, 517, 519, 543, 551, 553, 559, 565, 579, 597, 611, 623, 669, 685, 687
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
21: {2,4} 235: {3,15} 393: {2,32}
39: {2,6} 237: {2,22} 417: {2,34}
57: {2,8} 247: {6,8} 427: {4,18}
65: {3,6} 259: {4,12} 445: {3,24}
87: {2,10} 267: {2,24} 453: {2,36}
91: {4,6} 299: {6,9} 481: {6,12}
111: {2,12} 301: {4,14} 489: {2,38}
115: {3,9} 303: {2,26} 497: {4,20}
129: {2,14} 305: {3,18} 515: {3,27}
133: {4,8} 319: {5,10} 517: {5,15}
159: {2,16} 321: {2,28} 519: {2,40}
183: {2,18} 339: {2,30} 543: {2,42}
185: {3,12} 365: {3,21} 551: {8,10}
203: {4,10} 371: {4,16} 553: {4,22}
213: {2,20} 377: {6,10} 559: {6,14}
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MATHEMATICA
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Select[Range[100], SquareFreeQ[#]&&PrimeOmega[#]==2&&GCD@@PrimePi/@First/@FactorInteger[#]>1&]
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CROSSREFS
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A338909 is the not necessarily squarefree version.
A339005 lists products of pairs of distinct primes of divisible index.
A320656 counts factorizations into squarefree semiprimes.
A338910/A338911 list products of pairs of primes both of odd/even index.
Cf. A001221, A001222, A055684, A056239, A112798, A115392, A166237, A167171, A318990, A320892, A320911, A338901.
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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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