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A062373
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Ratio of totient to Carmichael's lambda function is 2.
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15
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8, 12, 15, 16, 20, 21, 28, 30, 32, 33, 35, 36, 39, 42, 44, 45, 51, 52, 55, 57, 64, 66, 68, 69, 70, 75, 76, 77, 78, 87, 90, 92, 93, 95, 99, 100, 102, 108, 110, 111, 114, 115, 116, 119, 123, 124, 128, 129, 135, 138, 141, 143, 147, 148, 150, 153, 154, 155, 159, 161
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OFFSET
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1,1
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COMMENTS
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Numbers k such that the highest order of elements in (Z/kZ)* is phi(n)/2, (Z/kZ)* = the multiplicative group of integers modulo k. Also numbers k such that (Z/kZ)* = C_2 X C_(2r). - Jianing Song, Jul 28 2018
Contains the powers of 2 greater than 4, 4 times primes, and semiprimes pq where (p-1)/2 and (q-1)/2 are coprime. If n is odd and in this sequence then so is 2n. - Charlie Neder, May 27 2019
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LINKS
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FORMULA
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Solutions to phi(k)/lambda(k) = 2.
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EXAMPLE
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(Z/8Z)* = C_2 X C_2, so 8 is a term.
(Z/21Z)* = C_2 X C_6, so 21 is a term.
(Z/35Z)* = C_2 X C_12, so 35 is a term. (End)
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MATHEMATICA
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Reap[ For[ n = 1, n <= 161, n++, If[ EulerPhi[n] / CarmichaelLambda[n] == 2, Sow[n]]]][[2, 1]] (* Jean-François Alcover, Mar 26 2013 *)
Select[Range[200], EulerPhi[#]/CarmichaelLambda[#]==2&] (* Harvey P. Dale, Jun 27 2018 *)
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PROG
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(Haskell)
a062373 n = a062373_list !! (n-1)
a062373_list = filter ((== 2) . a034380) [1..]
(PARI) isok(n) = eulerphi(n)/lcm(znstar(n)[2]) == 2; \\ Michel Marcus, Jul 28 2018
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CROSSREFS
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KEYWORD
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easy,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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