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A072296
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Least number starting a chain of exactly n consecutive even integers that do not have cototient-inverses.
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2
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10, 50, 532, 2314, 4628, 22578, 115024, 221960, 478302, 3340304, 22527850, 117335136, 1118736102, 1564578508, 6121287812, 7515991946
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OFFSET
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1,1
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COMMENTS
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If the strong Goldbach conjecture (every even number>6 is the sum of at least 2 distinct primes p and q) is true, sequence contains only even values. Since p*q-phi(p*q)=p+q-1 and then every odd number can be expressed as x-phi(x). - Benoit Cloitre, Mar 03 2002.
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LINKS
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EXAMPLE
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Neither 50 nor 52 have cototient-inverses and since 50 is the first of the two and the least number with this property, a(2) = 50.
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MATHEMATICA
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a = Table[0, {5*10^7}]; Do[b = n - EulerPhi[n]; If[ b < 5*10^7 + 1, a[[b/2]]++ ], {n, 2, 615437100}] (* used to find a(7) *) Do[ If[ a[[n]] == a[[n + 1]] == a[[n + 2]] == a[[n + 3]] == a[[n + 4]] == a[[n + 5]] == a[[n + 6]] == 0, Print[n]], {n, 1, 10^6}]
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CROSSREFS
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KEYWORD
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hard,more,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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