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A105783 Number of terms among the first n primes that are divisors of the sum of the first n primes.

%I A105783 #12 Jun 19 2018 05:08:38
%S A105783 1,0,2,0,2,0,1,2,2,1,2,0,3,0,2,1,3,1,1,2,1,1,3,1,3,2,2,1,3,2,3,1,3,1,
%T A105783 1,1,3,2,3,2,3,1,3,1,3,1,2,2,3,3,3,2,4,1,1,3,4,2,1,0,2,1,2,0,1,2,2,3,
%U A105783 2,3,3,1,3,1,1,2,4,1,3,3,1,1,1,4,3,2,4,3,3,3,4,1,1,2,1,0,2,3,2,0,2,0,4,1,4
%N A105783 Number of terms among the first n primes that are divisors of the sum of the first n primes.
%C A105783 Sequence inspired by A102863 (Giovanni Teofilatto).
%H A105783 Alois P. Heinz, <a href="/A105783/b105783.txt">Table of n, a(n) for n = 1..20000</a>
%e A105783 a(2)=0 because neither 2 nor 3 is a divisor of 5;
%e A105783 a(5)=2 because exactly two terms from {2,3,5,7,11} are divisors of 2+3+5+7+11=28.
%p A105783 with(numtheory): a:=n->nops(factorset(sum(ithprime(k),k=1..n)) intersect {seq(ithprime(j),j=1..n)}): seq(a(n),n=1..130);
%p A105783 # second Maple program:
%p A105783 s:= proc(n) option remember; `if`(n<1, 0, ithprime(n)+s(n-1)) end:
%p A105783 a:= n-> nops(select(x-> x <= ithprime(n), numtheory[factorset](s(n)))):
%p A105783 seq(a(n), n=1..100);  # _Alois P. Heinz_, Apr 11 2018
%t A105783 a[n_] := Module[{pp = Prime[Range[n]], s}, s = Total[pp]; Count[pp, p_ /; Divisible[s, p]]];
%t A105783 Array[a, 105] (* _Jean-François Alcover_, Jun 19 2018 *)
%o A105783 (PARI) a(n) = #select(x->(x <= prime(n)), factor(sum(k=1, n, prime(k)))[,1]); \\ _Michel Marcus_, Apr 11 2018
%Y A105783 Cf. A102863.
%K A105783 nonn
%O A105783 1,3
%A A105783 _Emeric Deutsch_, Apr 19 2005