A270415 Numbers n such that sigma(n-1) and sigma(n) - 1 are both primes.

3, 5, 10, 17, 26, 65, 65537, 146690, 703922, 1481090, 1885130, 2036330, 2211170, 2430482, 2505890, 5470922, 9840770, 11607650, 17783090, 24137570, 74425130, 76615010, 77563250, 133379402, 138697730, 138980522, 142396490, 155575730, 177715562, 181899170

Offset: 1

Author

Jaroslav Krizek, Mar 16 2016

Keywords

• nonn

Comments

Numbers n such that A000203(n-1) and A039653(n) are both primes.

Intersection of A270413 and A248792.

Prime terms are in A249759.

Corresponding values of sigma(n-1): 3, 7, 13, 31, 31, 127, 131071, ...

Corresponding values of sigma(n) - 1: 3, 5, 17, 17, 41, 83, 65537, ...

Examples

			17 is in the sequence because sigma(17-1) = sigma(16) = 31 and sigma(10) - 1 = 18 - 1 = 17 (both primes).
		

Crossrefs

Cf. A000203, A039653, A248792, A249759, A270413.

Programs

Magma

[n: n in [2..10000000] | IsPrime(SumOfDivisors(n-1)) and  IsPrime(SumOfDivisors(n)-1)];

Mathematica

Select[Range[10^7], And[PrimeQ@ DivisorSigma[1, # - 1], PrimeQ[DivisorSigma[1, #] - 1]] &] (* Michael De Vlieger, Mar 17 2016 *)

PARI

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