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A266165
Numbers n such that n = 2* phi(sigma((n-1)/2)) + 1.
0
3, 5, 17, 25, 257, 481, 1441, 13825, 65537, 285121, 1425601, 2280961, 2380801, 6690817, 7142401, 11404801, 29719873, 59439745, 100638721, 237758977, 4294967297, 7778073601, 8778792961
OFFSET
1,1
COMMENTS
Prime terms are in A260476.
The first 5 known Fermat primes from A019434 are in the sequence.
100638721, 8778792961 and 184354652161 are also terms.
EXAMPLE
17 = 2*phi(sigma((17-1)/2) + 1 = 2*phi(15) + 1 = 2*8 + 1, so 17 is in the sequence.
MATHEMATICA
Select[Range[10000], # == 2*EulerPhi[DivisorSigma[1, (# - 1)/2] ] + 1 &] (* G. C. Greubel, Dec 22 2015 *)
PROG
(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
(PARI) is(n)=n%2 && n>2 && 2*eulerphi(sigma((n-1)/2)) + 1 == n \\ Charles R Greathouse IV, Apr 25 2016
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Dec 22 2015
EXTENSIONS
More terms from Dana Jacobsen, Dec 27 2015
STATUS
approved