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Number of distinct prime factors of sum of 2 successive primes.
8

%I #30 Jan 20 2025 05:34:23

%S 1,1,2,2,2,3,2,3,2,3,2,3,3,3,2,2,3,1,3,2,2,2,2,3,3,3,4,2,3,3,3,2,3,2,

%T 3,3,2,4,3,2,3,3,2,4,3,3,3,3,3,4,2,3,3,2,3,3,3,2,3,3,2,3,3,3,4,2,2,3,

%U 3,3,2,3,3,2,3,2,3,4,3,3,4,3,2,2,3,2,3,3,4,4,3,4,3,4,3,3,3,3,3,2,3,3,2,4,3

%N Number of distinct prime factors of sum of 2 successive primes.

%H G. C. Greubel, <a href="/A071215/b071215.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = omega(prime(n) + prime(n + 1)) = A001221(A001043(n)), where omega is the number of distinct prime factors function.

%e Prime(6) = 13 and prime(7) = 17. 13 + 17 = 30 = 2 * 3 * 5, which has three distinct prime factors, hence a(6) = 3.

%t Table[PrimeNu[Prime[n] + Prime[n + 1]], {n, 105}] (* _Jean-François Alcover_, Oct 21 2013 *)

%o (PARI) A071215(n)=omega(prime(n)+prime(n+1)) \\ _M. F. Hasler_, Jul 23 2007

%Y Cf. A001043, A001221, A071216, A251609 (greedy inverse).

%K easy,nonn

%O 1,3

%A _Labos Elemer_, May 17 2002