This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Join[{1},Flatten[Position[Accumulate[Prime[Range[80]]],?CompositeQ]]] (* _Harvey P. Dale, Apr 23 2015 *)
a(2)=0 because neither 2 nor 3 is a divisor of 5;
a(5)=2 because exactly two terms from {2,3,5,7,11} are divisors of 2+3+5+7+11=28.
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);
# second Maple program:
s:= proc(n) option remember; `if`(n<1, 0, ithprime(n)+s(n-1)) end:
a:= n-> nops(select(x-> x <= ithprime(n), numtheory[factorset](s(n)))):
seq(a(n), n=1..100); # Alois P. Heinz, Apr 11 2018
a[n_] := Module[{pp = Prime[Range[n]], s}, s = Total[pp]; Count[pp, p_ /; Divisible[s, p]]];
Array[a, 105] (* Jean-François Alcover, Jun 19 2018 *)
a(n) = #select(x->(x <= prime(n)), factor(sum(k=1, n, prime(k)))[,1]); \\ Michel Marcus, Apr 11 2018
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