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A175767
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List of pairs of "twin numbers": Omega(n) = Omega(n - 2^Omega(n)), where Omega is A001222.
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0
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3, 5, 5, 7, 6, 10, 11, 13, 10, 14, 17, 19, 12, 20, 21, 25, 22, 26, 20, 28, 29, 31, 34, 38, 35, 39, 24, 40, 41, 43, 42, 50, 44, 52, 51, 55, 40, 56, 59, 61, 58, 62, 65, 69, 71, 73, 68, 76, 70, 78, 48, 80, 82, 86, 87, 91, 91, 95, 84, 100, 101, 103, 88, 104, 107, 109, 102, 110, 80, 112, 111
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OFFSET
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1,1
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COMMENTS
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The k-primes = numbers that are divisible by exactly k primes (counted with multiplicity).
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LINKS
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FORMULA
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EXAMPLE
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"Twin numbers" are (3, 5), (5, 7), (6, 10), (11, 13), (10, 14), (17, 19), (12, 20), (21, 25), (22, 26), (20, 28), (29, 31), (34, 38), (35, 39), (24, 40), (41, 43), (42, 50), (44, 52), (51, 55), (40, 56), (59, 61), (58, 62), (65, 69), (71, 73), ...
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MATHEMATICA
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Flatten[{#[[3]], #[[1]]}&/@Select[Table[{n, PrimeOmega[n], n-2^PrimeOmega[n], PrimeOmega[ n-2^PrimeOmega[n]]}, {n, 150}], #[[2]]==#[[4]]&]] (* Harvey P. Dale, Mar 23 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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