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A093429
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Number of distinct prime factors of (prime(1)*...*prime(n))+(prime(n+1)*...*prime(2n)), where prime(n) is the n-th prime.
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1
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1, 1, 1, 1, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 4, 3, 2, 6, 3, 4, 4, 3, 1, 1, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 5, 4, 2, 3, 3, 5, 3, 7, 4, 1, 4, 3, 4, 3, 6, 2, 4, 3, 3
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OFFSET
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1,5
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COMMENTS
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Prime for n = 1, 2, 3, 4, 24, 25, 45, 59 and no more for n < 100 (A329532).
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LINKS
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Cashogor, Payam Samidoost, David Cleaver, Jens Kruse Andersen, Creating Primes, digest of 9 messages in primeforms Yahoo group, May 12, 2004. [Cached copy]
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FORMULA
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EXAMPLE
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a(31)=4 because 509102378439545188849067644696085192959414195658632710736111053092210207
= 3711597629 * 238694867020723 * 226814268663739929299 * 2533557617597929944840907379.
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MATHEMATICA
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PrimeFactors[n_] := Flatten[ Table[ # [[1]], {1} ] & /@ FactorInteger[n]]; f[n_] := Length[ PrimeFactors[ Product[Prime[i], {i, n}] + Product[Prime[i + n], {i, n}]]]; Table[ f[n], {n, 20}]
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PROG
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(PARI) a(n) = omega(prod(k=1, n, prime(k)) + prod(k=n+1, 2*n, prime(k))); \\ Daniel Suteu, Nov 26 2019
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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