A260476 Primes p such that p = 2*phi(sigma((p-1)/2))+ 1.

3, 5, 17, 257, 65537, 285121, 1425601, 2380801, 100638721, 8778792961, 184354652161

Offset

1,1

Comments

The first 5 known Fermat primes from A019434 are in sequence.

Links

Table of n, a(n) for n=1..11.

Example

17 = 2*phi(sigma((17-1)/2)+1 = 2*phi(15)+1 = 2*8+1, so 17 is in the sequence.

Mathematica

Select[Prime@ Range@ 1000000, # == 2 EulerPhi[DivisorSigma[1, (# - 1)/2]] + 1 &] (* Michael De Vlieger, Sep 25 2015 *)

Prog

(Magma) [n: n in [3..1000000] | IsPrime(n) and n eq 2 * EulerPhi(SumOfDivisors((n-1) div 2)) + 1]
(PARI) forprime(p=3, 1e8, if((2*eulerphi(sigma((p-1)/2)) + 1) == p, print1(p ", "))) \\ Altug Alkan, Sep 25 2015

Crossrefs

Cf. A019434, A062401.

Sequence in context: A093179 A067387 A050922 * A070592 A254576 A232720

Adjacent sequences: A260473 A260474 A260475 * A260477 A260478 A260479

Keyword

nonn,more

Author

Jaroslav Krizek, Sep 24 2015

Status

approved