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A105783
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Number of terms among the first n primes that are divisors of the sum of the first n primes.
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3
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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
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OFFSET
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1,3
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COMMENTS
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Sequence inspired by A102863 (Giovanni Teofilatto).
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LINKS
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EXAMPLE
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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.
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MAPLE
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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)))):
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MATHEMATICA
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a[n_] := Module[{pp = Prime[Range[n]], s}, s = Total[pp]; Count[pp, p_ /; Divisible[s, p]]];
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PROG
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(PARI) a(n) = #select(x->(x <= prime(n)), factor(sum(k=1, n, prime(k)))[, 1]); \\ Michel Marcus, Apr 11 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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