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A338908
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Squarefree semiprimes whose prime indices sum to an even number.
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13
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10, 21, 22, 34, 39, 46, 55, 57, 62, 82, 85, 87, 91, 94, 111, 115, 118, 129, 133, 134, 146, 155, 159, 166, 183, 187, 194, 203, 205, 206, 213, 218, 235, 237, 247, 253, 254, 259, 267, 274, 295, 298, 301, 303, 314, 321, 334, 335, 339, 341, 358, 365, 371, 377, 382
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OFFSET
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1,1
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COMMENTS
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A squarefree semiprime is a product of any two distinct prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
10: {1,3} 115: {3,9} 213: {2,20}
21: {2,4} 118: {1,17} 218: {1,29}
22: {1,5} 129: {2,14} 235: {3,15}
34: {1,7} 133: {4,8} 237: {2,22}
39: {2,6} 134: {1,19} 247: {6,8}
46: {1,9} 146: {1,21} 253: {5,9}
55: {3,5} 155: {3,11} 254: {1,31}
57: {2,8} 159: {2,16} 259: {4,12}
62: {1,11} 166: {1,23} 267: {2,24}
82: {1,13} 183: {2,18} 274: {1,33}
85: {3,7} 187: {5,7} 295: {3,17}
87: {2,10} 194: {1,25} 298: {1,35}
91: {4,6} 203: {4,10} 301: {4,14}
94: {1,15} 205: {3,13} 303: {2,26}
111: {2,12} 206: {1,27} 314: {1,37}
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MATHEMATICA
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Select[Range[100], SquareFreeQ[#]&&PrimeOmega[#]==2&& EvenQ[Total[PrimePi/@First/@FactorInteger[#]]]&]
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CROSSREFS
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A031215 looks at primes instead of semiprimes.
A300061 and A319241 (squarefree) look all numbers (not just semiprimes).
A338905 has this as union of even-indexed rows.
A338906 is the nonsquarefree version.
A024697 is the sum of semiprimes of weight n.
A025129 is the sum of squarefree semiprimes of weight n.
A056239 gives the sum of prime indices of n.
A320656 counts factorizations into squarefree semiprimes.
A332765 gives the greatest squarefree semiprime of weight n.
A338904 groups semiprimes by weight.
A338911 lists products of pairs of primes both of even index.
A339116 groups squarefree semiprimes by greater prime factor.
Cf. A000040, A001221, A001222, A087112, A098350, A112798, A168472, A338901, A338904, A339004, A339005.
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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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