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Search: id:A108569
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| A108569 |
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Numbers n such that phi(n) = phi(n + phi(n)). |
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1
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| 1, 4, 8, 16, 32, 64, 110, 128, 220, 256, 440, 506, 512, 550, 880, 1012, 1024, 1100, 1760, 1830, 2024, 2048, 2162, 2200, 2750, 3422, 3520, 3660, 4048, 4096, 4114, 4324, 4400, 4746, 5490, 5500, 5566, 6806, 6844, 7040, 7320, 7782, 8096, 8192, 8228, 8648, 8800
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OFFSET
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1,2
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COMMENT
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If n is an even term of this sequence then 2n is also in the sequence. Because phi(2n)=2*phi(n)=2*phi(n+phi(n))=phi(2n+ 2*phi(n))=phi(2n+phi(2n)). So if n is an even term of this sequence then for each natural number m, 2^m*n is in the sequence. For example since 4 is in the sequence 2^n for each n, n>1 is in the sequence. If p is a Sophie Germain prime greater than 3 then n=2*p*(2p+1) is in the sequence because phi(n+phi(n))=phi(2*p*(2p+1)+2*p* (p-1))=phi(6p^2)=2*p*(p-1)=phi(n). Conjecture : Except for the first term all terms are even.
If n is in the sequence and the natural number m divides gcd(phi(n),n) then for all nonnegative integers k, m^k*n are in the sequence For example 110 is in the sequence and 10 divides gcd(phi(110),110) so 11*10^k for all natural numbers k are in the sequence. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Dec 12 2005
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MATHEMATICA
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Select[Range[11000], EulerPhi[ # ]==EulerPhi[ # + EulerPhi[ # ]]&]
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CROSSREFS
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Cf. A005384, A051487.
Sequence in context: A036313 A121986 A145108 this_sequence A111073 A005934 A085629
Adjacent sequences: A108566 A108567 A108568 this_sequence A108570 A108571 A108572
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KEYWORD
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nonn
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AUTHOR
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Farideh Firoozbakht (mymontain(AT)yahoo.com), Jul 05 2005
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