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%I #26 Jul 09 2023 09:27:52
%S 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,
%T 3,5,4,2,3,3,5,3,7,4,1,4,3,4,3,6,2,4,3,3
%N Number of distinct prime factors of (prime(1)*...*prime(n))+(prime(n+1)*...*prime(2n)), where prime(n) is the n-th prime.
%C Prime for n = 1, 2, 3, 4, 24, 25, 45, 59 and no more for n < 100 (A329532).
%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>.
%H P. Samidoost, <a href="http://groups.yahoo.com/group/primenumbers/message/14849">Primenumbers group posting</a>.
%H Cashogor, Payam Samidoost, David Cleaver, Jens Kruse Andersen, <a href="/A329532/a329532.txt">Creating Primes</a>, digest of 9 messages in primeforms Yahoo group, May 12, 2004. [Cached copy]
%F a(n) = A001221(A002110(n) + A002110(2*n) / A002110(n)). - _Daniel Suteu_, Nov 26 2019
%e a(31)=4 because 509102378439545188849067644696085192959414195658632710736111053092210207
%e = 3711597629 * 238694867020723 * 226814268663739929299 * 2533557617597929944840907379.
%t 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}]
%o (PARI) a(n) = omega(prod(k=1, n, prime(k)) + prod(k=n+1, 2*n, prime(k))); \\ _Daniel Suteu_, Nov 26 2019
%Y Cf. A001221, A002110, A093433, A329532.
%K nonn,more
%O 1,5
%A _Jason Earls_, May 12 2004
%E a(40)-a(48) from _Robert G. Wilson v_, May 27 2004
%E a(49)-a(54) from _Daniel Suteu_, Nov 26 2019
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