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

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, 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, 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

Offset: 1

Author

Emeric Deutsch, Apr 19 2005

Keywords

• nonn

Comments

Sequence inspired by A102863 (Giovanni Teofilatto).

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A102863.

Programs

Maple

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

Mathematica

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 *)

PARI

a(n) = #select(x->(x <= prime(n)), factor(sum(k=1, n, prime(k)))[,1]); \\ Michel Marcus, Apr 11 2018