%I #7 Apr 18 2021 22:33:43

%S 11,29,41,61,73,97,131,137,139,149,151,157,167,179,191,211,227,229,

%T 233,241,251,283,293,307,313,331,347,373,383,389,397,401,449,463,521,

%U 577,607,631,641,647,653,661,673,677,701,709,719,727,757,769,811,821,823,829,857,859,877,887,907,919,929

%N Primes that occur in A343416.

%C Terms are distinct and in numerical order, not the order they occur in A343416.

%C If p, 6*p-1 and 19*p+4 are prime, then 19*p+4 = A343416(6*p-1) is a term. Dickson's conjecture implies that there are infinitely many such terms.

%H Robert Israel, <a href="/A343418/b343418.txt">Table of n, a(n) for n = 1..4000</a>

%e a(3) = 41 is a term because 41 = A343416(8) = A343416(10) and is prime.

%p spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:

%p f:= proc(n) local a,b;

%p a:= spf(n);

%p b:= numtheory:-sigma(n);

%p a+b+spf(b)+numtheory:-sigma(a)

%p end proc:

%p S:= select(t -> t < 1000 and isprime(t), map(f, {$1..1000})):

%p sort(convert(S,list));

%Y Cf. A343416.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Apr 14 2021