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A266165
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Numbers n such that n = 2* phi(sigma((n-1)/2)) + 1.
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0
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3, 5, 17, 25, 257, 481, 1441, 13825, 65537, 285121, 1425601, 2280961, 2380801, 6690817, 7142401, 11404801, 29719873, 59439745, 100638721, 237758977, 4294967297, 7778073601, 8778792961
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OFFSET
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1,1
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COMMENTS
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The first 5 known Fermat primes from A019434 are in the sequence.
100638721, 8778792961 and 184354652161 are also terms.
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LINKS
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EXAMPLE
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17 = 2*phi(sigma((17-1)/2) + 1 = 2*phi(15) + 1 = 2*8 + 1, so 17 is in the sequence.
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MATHEMATICA
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Select[Range[10000], # == 2*EulerPhi[DivisorSigma[1, (# - 1)/2] ] + 1 &] (* G. C. Greubel, Dec 22 2015 *)
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PROG
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(Magma) [n: n in [3..10^7] | n eq 2*EulerPhi(SumOfDivisors((n-1) div 2)) + 1]
(Perl) use ntheory ":all"; for (1..1e7) { say if 2*euler_phi(divisor_sum(($_-1)>>1))+1 == $_ } # Dana Jacobsen, Dec 27 2015
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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