cp's OEIS Frontend

A340062 Averages k of twin primes such that the sum (with multiplicity) of prime factors of k-1, k and k+1 is a prime power (but not a prime).

%I A340062 #10 Jan 09 2021 02:12:08
%S A340062 39372,104963700,116479500,182003250,202991022,231362100
%N A340062 Averages k of twin primes such that the sum (with multiplicity) of prime factors of k-1, k and k+1 is a prime power (but not a prime).
%e A340062 a(3) = 116479500 is a member because 116579499 and 11657501 are primes and the sum of prime factors of 116579499, 116579500 = 2^2*3*5^3*19*61*67 and 116579501 is 232959169 = 15263^2 where 15263 is prime.
%p A340062 filter:= proc(t)
%p A340062 local r,s,f;
%p A340062   if not(isprime(t-1) and isprime(t+1)) then return false fi;
%p A340062   r:= 2*t+add(s[1]*s[2],s=ifactors(t)[2]);
%p A340062   f:=numtheory:-factorset(r);
%p A340062   nops(f) = 1 and r <> f[1]
%p A340062 end proc:
%p A340062 select(filter, [seq(t,t=6..3*10^8,6)]);
%Y A340062 Cf. A001414, A340060.
%K A340062 nonn,more
%O A340062 1,1
%A A340062 _J. M. Bergot_ and _Robert Israel_, Dec 27 2020