A086715 - OEIS

%I #16 Sep 08 2022 08:45:11

%S 11,53,89,251,359,383,389,463,487,809,857,863,1109,1217,1429,1451,

%T 1549,2039,2089,2459,2903,3037,3457,3541,3709,3727,3739,4259,4373,

%U 4451,4733,4903,5641,5851,5939,6359,7019,7079,7129,7219,7549,8059,8839,8929,9007

%N Primes p such that A001414(p-1) and A001414(p+1) are both prime, where A001414 = sum of primes dividing n (with repetition).

%H Amiram Eldar, <a href="/A086715/b086715.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2)=53 because it is prime and 52=2^2*13, 54=2*3^3 and 2+2+13=17 and 2+3+3+3=11.

%t primeSopfQ[n_] := PrimeQ[Plus @@ Times @@@ FactorInteger[n]]; seqQ[n_] := PrimeQ[n] && AllTrue[{n - 1, n + 1}, primeSopfQ];  Select[Range[10^4], seqQ] (* _Amiram Eldar_, Dec 14 2019 *)

%o (Magma) [ n : n in [3..9100] | IsPrime(n) and IsPrime(&+[ k[1]*k[2] : k in Factorization(n-1)]) and IsPrime(&+[ k[1]*k[2] : k in Factorization(n+1)]) ]; /* _Klaus Brockhaus_, Mar 24 2007 */

%Y Cf. A001414.

%K easy,nonn

%O 1,1

%A _Jason Earls_, Jul 29 2003

%E Checked by _Klaus Brockhaus_, Mar 24 2007