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A259643
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Numbers n such that sum of first n odd primes divides product of first n odd primes.
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1
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1, 3, 5, 11, 25, 29, 41, 49, 51, 59, 69, 81, 99, 103, 113, 131, 133, 135, 147, 149, 153, 181, 187, 193, 197, 199, 205, 211, 213, 217, 219, 229, 235, 239, 243, 255, 271, 277, 281, 287, 289, 303, 309, 313, 323, 333, 335, 343, 347, 357, 359, 365, 367, 381, 383, 389
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OFFSET
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1,2
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COMMENTS
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Obviously, a(n) is always an odd number.
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LINKS
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EXAMPLE
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a(1) = 1 because prime(2) mod prime(2) = 3 mod 3 = 0.
a(2) = 3 because (prime(2) * prime(3) * prime(4)) mod (prime(2) + prime(3) + prime(4)) = 105 mod 15 = 0.
a(3) = 5 because (prime(2) * prime(3) * prime(4) * prime(5) * prime(6)) mod (prime(2) + prime(3) + prime(4) + prime(5) + prime(6)) = 15015 mod 39 = 0.
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MATHEMATICA
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Module[{nn=400, op}, op=Prime[Range[2, nn+1]]; Select[Range[nn], Divisible[ Times@@ Take[op, #], Total[Take[op, #]]]&]] (* Harvey P. Dale, Nov 16 2022 *)
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PROG
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for(n=1, 1e3, if( prod(k=1, n, prime(k+1)) % sum(k=1, n, prime(k+1)) == 0 , print1(n", ")))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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