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 A105783 Number of terms among the first n primes that are divisors of the sum of the first n primes. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Sequence inspired by A102863 (Giovanni Teofilatto). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..20000 EXAMPLE 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. 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 *) PROG (PARI) a(n) = #select(x->(x <= prime(n)), factor(sum(k=1, n, prime(k)))[, 1]); \\ Michel Marcus, Apr 11 2018 CROSSREFS Cf. A102863. Sequence in context: A086150 A105166 A321299 * A326819 A268189 A265247 Adjacent sequences:  A105780 A105781 A105782 * A105784 A105785 A105786 KEYWORD nonn AUTHOR Emeric Deutsch, Apr 19 2005 STATUS approved

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)