A171130 -id:A171130 - cp's OEIS frontend

A171131 Primes p such that sum of divisors of p-3 is prime.

5, 7, 19, 67, 4099, 65539, 262147, 1073741827

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 04 2009

nonn

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

			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.

Cf. A000043, A000203, A023194, A057732, A171130, A153503.

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 *)

a(8)-a(10) from Vincenzo Librandi, Feb 04 2013

Two wrong terms removed by Amiram Eldar, Aug 01 2024

A247955 Primes p such that there is prime q with sigma(q+2) = p.

Original entry on oeis.org

7, 13, 31, 1093, 2801, 5113, 8011, 17293, 30103, 30941, 86143, 459007, 552793, 579883, 732541, 1191373, 3500201, 3730693, 4534771, 5168803, 5333791, 7450171, 10378063, 25646167, 25882657, 28792661, 30266503, 43553401, 48037081, 52265671, 56964757, 62433703, 65504743, 67856407, 76413823, 77572057

Offset: 1

Jaroslav Krizek, Sep 28 2014

nonn

Primes p such that there is prime q such that A000203(q+2) = p.

Primes p of the form sigma(A171130(n)) in increasing order.

Cf. A000203, A008438, A171130, A247791, A247820, A247821, A247822, A247823, A247954.

Sort[Select[DivisorSigma[1,#+2]&/@Prime[Range[5200000]],PrimeQ]] (* Harvey P. Dale, Apr 27 2022 *)

v=[];forprime(p=1,10^8,if(ispseudoprime(sigma(p+2)),v=concat(v,sigma(p+2))));v \\ Derek Orr, Oct 26 2014

More terms from Michel Marcus, Oct 02 2014

Corrected and extended by Harvey P. Dale, Apr 27 2022

cp's OEIS Frontend

A171131 Primes p such that sum of divisors of p-3 is prime.

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