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A277366
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Composite numbers k such that phi(k)*lambda(k) divides (k-1)^2, where phi(k) = A000010(k) and lambda(k) = A002322(k).
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1
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1729, 670033, 6840001, 83099521, 193708801, 321197185, 367804801, 484662529, 1752710401, 2320690177, 5064928705, 12820178449, 32220147601, 257124585601, 270177600001, 301036080385, 7043394657601, 13237329899521, 14276860416001, 85661522006401, 119377939968001
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OFFSET
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1,1
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COMMENTS
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Are there infinitely many such numbers?
Such k must be a Carmichael number since phi(k)*lambda(k) = m*lambda(k)^2 for some integer m. - Nathan McNew, Oct 11 2016
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LINKS
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MATHEMATICA
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Select[Range[10^8], CompositeQ[#] && Divisible[(# - 1)^2, EulerPhi[#] * CarmichaelLambda[#]] &] (* Amiram Eldar, Feb 02 2019 *)
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PROG
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(PARI) lista(nn) = forcomposite(n=4, nn, if (((n-1)^2 % (eulerphi(n)*lcm(znstar(n)[2]))) == 0, print1(n, ", ")); ); \\ Michel Marcus, Oct 11 2016
(PARI) is(n, f=factor(n))=(n-1)^2%(eulerphi(f)*lcm(znstar(f)[2])) == 0 && !isprime(n) && n>1 \\ Charles R Greathouse IV, Oct 11 2016
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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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