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

1,1

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, ...

Links

Table of n, a(n) for n=1..30.

Example

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

Mathematica

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

Prog

(Magma) [n: n in [2..10000000] | IsPrime(SumOfDivisors(n-1)) and  IsPrime(SumOfDivisors(n)-1)]
(PARI) isok(n) = isprime(sigma(n-1)) && isprime(sigma(n)-1); \\ Michel Marcus, Mar 17 2016

Crossrefs

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

Sequence in context: A310019 A261998 A270413 * A192757 A079934 A215004

Adjacent sequences: A270412 A270413 A270414 * A270416 A270417 A270418

Keyword

nonn

Author

Jaroslav Krizek, Mar 16 2016

Status

approved