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%I #14 Oct 21 2015 18:04:11
%S 1,2,4,6,40,43,705,789,1148,2140,4276,5512,6672,8754,38434,174501,
%T 493578,598249,628064,702774,1368196,4584004,13813057,36425906,
%U 87964443,447997476,1964288296
%N Numbers k such that k divides the sum of the first k primes with prime indices.
%C There are 8 values of a(n) < 1000 although A045345 has 4 values A045345(n) < 1000. How do these sequences compare asymptotically?
%C Heuristics suggest that the ratio of the number of terms in each sequence up to x should approach 1 as x increases without bound. In the Cramér model, log a(n) and log A045345(n) are Erlang-distributed with shape n and rate 1. - _Charles R Greathouse IV_, Oct 20 2015
%e 1 is in the sequence because prime(prime(1)) = 3 is divisible by 1.
%e 2 is in the sequence because prime(prime(1)) + prime(prime(2)) = 3 + 5 = 8 is divisible by 2.
%o (PARI) list(lim)=my(v=List(),k,s,t); forprime(p=2,, if(isprime(t++), s+=p; k++; if(s%k==0, listput(v, k)); if(k>=lim, return(Vec(v))))) \\ _Charles R Greathouse IV_, Oct 20 2015
%Y Cf. A006450, A045345, A083186.
%K nonn
%O 1,2
%A _Altug Alkan_, Oct 20 2015
%E a(12)-a(26) from _Charles R Greathouse IV_, Oct 20 2015
%E a(27) from _Charles R Greathouse IV_, Oct 21 2015