A065875 Numbers k such that usigma(phi(k)) is a prime.

3, 4, 5, 6, 8, 10, 12, 17, 32, 34, 40, 48, 60, 257, 512, 514, 544, 640, 680, 768, 816, 960, 1020, 65537, 131072, 131074, 131584, 139264, 139808, 163840, 164480, 174080, 174760, 196608, 197376, 208896, 209712, 245760, 246720, 261120, 262140

Offset: 1

Author

Robert G. Wilson v, Dec 07 2001

Keywords

• nonn

Comments

The only odd terms below 10^7 are 3, 5, 17, 257 and 65537.

Numbers k such that phi(k) = 2^(2^m) where 2^(2^m)+1 is a Fermat prime (A019434). a(42) >= 2^(2^33) + 1, if a 6th Fermat prime exists. - Amiram Eldar, Dec 14 2024

Crossrefs

Cf. A062514, A034448, A000010, A019434.

Programs

PARI

u(n)=sumdivmult(n, d, if(gcd(d, n/d)==1, d));
for(n=1,10^5,if(isprime(u(eulerphi(n))),print1(n,", "))); \\ Joerg Arndt, Sep 17 2023

Extensions

Deleted incorrect MMA program. - N. J. A. Sloane, Sep 17 2023