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

1,1

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, ...

Links

Table of n, a(n) for n=1..41.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A230124 A027627 A194466 * A290269 A115059 A250218

Adjacent sequences: A270413 A270414 A270415 * A270417 A270418 A270419

Keyword

nonn

Author

Jaroslav Krizek, Mar 16 2016

Extensions

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

Status

approved