A270416 Numbers n such that sigma(n) - 1 and sigma(phi(n)) are both primes.

3, 5, 6, 10, 17, 34, 40, 60, 85, 136, 204, 240, 4369, 8224, 8704, 8738, 10880, 12336, 13056, 65537, 131074, 131584, 139264, 163840, 164480, 174760, 208896, 245760, 262140, 524296, 526336, 559232, 835584, 838848, 2281736192, 2694881440, 2852170240, 2863267840, 3221274624, 3233857728, 4026593280

Offset: 1

Author

Jaroslav Krizek, Mar 16 2016

Keywords

• nonn

Comments

Numbers n such that A039653(n) and A062402(n) are both primes.

Intersection of A248792 and A062514.

Prime terms are in A249759.

Corresponding values of sigma(n) - 1: 3, 5, 11, 17, 17, 53, 89, 167, ...

Corresponding values of sigma(phi(n)): 3, 7, 3, 7, 31, 31, 31, 31, 127, ...

Examples

			10 is in the sequence because sigma(10) - 1 = 18 - 1 = 17 and sigma(phi(10)) = sigma(4) = 7 (both primes).
		

Crossrefs

Cf. A000203, A039653, A062402, A062514, A248792, A249759.

Programs

Mathematica

Select[Range[10^6], And[PrimeQ[DivisorSigma[1, #] - 1], PrimeQ@ DivisorSigma[1, EulerPhi@ #]] &] (* Michael De Vlieger, Mar 17 2016 *)

PARI

isok(n) = isprime(sigma(n)-1) && isprime(sigma(eulerphi(n))); \\ Michel Marcus, Mar 17 2016

Extensions

a(35)-a(41) from Giovanni Resta, Apr 10 2016