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Numbers n such that sigma(n-1) and sigma(n) - 1 are both primes.
2

%I #9 Sep 08 2022 08:46:16

%S 3,5,10,17,26,65,65537,146690,703922,1481090,1885130,2036330,2211170,

%T 2430482,2505890,5470922,9840770,11607650,17783090,24137570,74425130,

%U 76615010,77563250,133379402,138697730,138980522,142396490,155575730,177715562,181899170

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

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

%C Intersection of A270413 and A248792.

%C Prime terms are in A249759.

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

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

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

%t Select[Range[10^7], And[PrimeQ@ DivisorSigma[1, # - 1], PrimeQ[DivisorSigma[1, #] - 1]] &] (* _Michael De Vlieger_, Mar 17 2016 *)

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

%o (PARI) isok(n) = isprime(sigma(n-1)) && isprime(sigma(n)-1); \\ _Michel Marcus_, Mar 17 2016

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

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Mar 16 2016