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A302567
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a(n) is the number of primes less than the n-th prime that divide the sum of primes up to the n-th prime.
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1
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0, 0, 1, 0, 2, 0, 1, 2, 2, 1, 2, 0, 3, 0, 2, 1, 3, 1, 1, 1, 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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1,5
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COMMENTS
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LINKS
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Caldwell and Honaker, Prime Curios!: 163117
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FORMULA
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EXAMPLE
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a(13)=3 because the 13th prime is 41 and the sum of primes up to 41 is 238, which has 3 distinct prime factors less than 41.
a(20)=1 because the 20th prime is 71 and the sum of primes up to 71 is 639 = 7*71, which has only 1 distinct prime factor less than 71. - Jon E. Schoenfield, Apr 11 2018
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MAPLE
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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_] := (S = Total[P = Prime[Range[n]]]; Count[P, 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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