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A338906
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Semiprimes whose prime indices sum to an even number.
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16
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4, 9, 10, 21, 22, 25, 34, 39, 46, 49, 55, 57, 62, 82, 85, 87, 91, 94, 111, 115, 118, 121, 129, 133, 134, 146, 155, 159, 166, 169, 183, 187, 194, 203, 205, 206, 213, 218, 235, 237, 247, 253, 254, 259, 267, 274, 289, 295, 298, 301, 303, 314, 321, 334, 335, 339
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OFFSET
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1,1
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COMMENTS
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A semiprime is a product of any two 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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FORMULA
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EXAMPLE
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The sequence of terms together with their prime indices begins:
4: {1,1} 87: {2,10} 183: {2,18} 274: {1,33}
9: {2,2} 91: {4,6} 187: {5,7} 289: {7,7}
10: {1,3} 94: {1,15} 194: {1,25} 295: {3,17}
21: {2,4} 111: {2,12} 203: {4,10} 298: {1,35}
22: {1,5} 115: {3,9} 205: {3,13} 301: {4,14}
25: {3,3} 118: {1,17} 206: {1,27} 303: {2,26}
34: {1,7} 121: {5,5} 213: {2,20} 314: {1,37}
39: {2,6} 129: {2,14} 218: {1,29} 321: {2,28}
46: {1,9} 133: {4,8} 235: {3,15} 334: {1,39}
49: {4,4} 134: {1,19} 237: {2,22} 335: {3,19}
55: {3,5} 146: {1,21} 247: {6,8} 339: {2,30}
57: {2,8} 155: {3,11} 253: {5,9} 341: {5,11}
62: {1,11} 159: {2,16} 254: {1,31} 358: {1,41}
82: {1,13} 166: {1,23} 259: {4,12} 361: {8,8}
85: {3,7} 169: {6,6} 267: {2,24} 365: {3,21}
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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[100], PrimeOmega[#]==2&&EvenQ[Total[primeMS[#]]]&]
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CROSSREFS
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A031215 looks at primes instead of semiprimes.
A098350 has this as union of even-indexed antidiagonals.
A300061 looks at all numbers (not just semiprimes).
A338904 has this as union of even-indexed rows.
A056239 gives the sum of prime indices (Heinz weight).
A087112 groups semiprimes by greater factor.
A338911 lists products of pairs of primes both of even index.
Cf. A000040, A001222, A024697, A037143, A112798, A300063, A319242, A320655, A332765, A338910, A339004.
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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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