A270414 Numbers m such that sigma(m-1) and sigma(phi(m)) are both primes.

3, 5, 10, 17, 65537

Offset: 1

Author

Jaroslav Krizek, Mar 16 2016

Keywords

• nonn
• more

Comments

Numbers n such that A000203(n-1) and A062402(n) are both primes.

There are no other terms <= 10^7.

Intersection of A270413 and A062514.

Prime terms are in A249759.

Corresponding values of sigma(n-1): 3, 7, 13, 31, 131071, ...

Corresponding values of sigma(phi(n)): 3, 7, 7, 31, 131071, ...

Conjecture: union of number 10 and A249759.

Examples

			10 is in the sequence because sigma(10-1) = sigma(9) = 13 and sigma(phi(10)) = sigma(4) = 7 (both primes).
		

Crossrefs

Cf. A000010, A000203, A062514, A249759, A256438, A270413.

Programs

Magma

[n: n in [2..100000] |  IsPrime(SumOfDivisors(n-1)) and IsPrime(SumOfDivisors(EulerPhi(n)))];

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