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A185165
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Numbers n such that lambda(n) = lambda(n - lambda(n)).
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2
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2, 6, 8, 20, 42, 75, 90, 117, 154, 156, 189, 220, 363, 385, 490, 525, 702, 775, 777, 845, 975, 990, 1050, 1183, 1276, 1300, 1505, 1587, 1628, 1742, 1806, 1824, 1860, 1905, 1911, 2436, 2496, 2523, 2541, 2793, 2860, 2943, 3660, 3720, 3800, 3960, 4309, 5043, 5060, 5390, 5540, 5994, 6069, 6160, 6664, 6845, 8127, 8268, 8325, 8427
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OFFSET
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1,1
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COMMENTS
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Lambda is the function in A002322. If there are infinitely many Sophie Germain primes (conjecture), then this sequence is infinite. Proof: The numbers of the form 3p^2 are in a subsequence if p and 2p+1 are both prime with p > 3, because from the property that lambda(3p^2) = p(p-1) and lambda (p(2p+1)) = p(p-1), if m = 3p^2 then lambda(m-phi(m)) = lambda (3p^2 - p(p-1)) = lambda(p(2p+1)) = p(p-1) = lambda(m).
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LINKS
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EXAMPLE
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75 is in the sequence because lambda(75) = 20, lambda(75 - 20) = lambda(55) = 20.
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MATHEMATICA
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Select[Range[20000], CarmichaelLambda[ #] == CarmichaelLambda[ # - CarmichaelLambda[#] ] &]
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CROSSREFS
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Cf. A051487 (numbers n such that phi(n) = phi(n - phi(n))).
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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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