OFFSET
1,1
COMMENTS
No further terms up to the 10 millionth prime. - Harvey P. Dale, Apr 30 2012
If the sum of divisors of a number k is a prime (i.e., k is in A023194), then k is a prime power. If p is prime and p-3 is a prime power, then p-3 is even, so p-3 is a power of 2. Since p-3 = 2^m then sigma(2^m) = 2^(m+1)-1 is a prime. Therefore, all the terms are primes of the form 2^m+3 where m+1 is a Mersenne exponent (A000043), i.e., m is in the intersection of A057732 and {A000043(n)-1}. So, m = 1, 2, 4, 6, 12, 16, 18, 30, and no other value <= A057732(58) = 2205444. Therefore, a(9) > 2^2205444, if it exists. - Amiram Eldar, Aug 01 2024
EXAMPLE
5 is a term since it is a prime and sigma(5-3) = 3 is a prime.
7 is a term since it is a prime and sigma(7-3) = 7 is a prime.
19 is a term since it is a prime and sigma(19-3) = 31 is a prime.
MATHEMATICA
f[n_]:=Plus@@Divisors[n]; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p-3]], AppendTo[lst, p]], {n, 2*10!}]; lst
Select[Prime[Range[10000000]], PrimeQ[DivisorSigma[1, #-3]]&] (* Harvey P. Dale, Apr 30 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Dec 04 2009
EXTENSIONS
a(8)-a(10) from Vincenzo Librandi, Feb 04 2013
Two wrong terms removed by Amiram Eldar, Aug 01 2024
STATUS
approved