A098037 Number of prime divisors, counted with multiplicity, of the sum of two consecutive primes.

1, 3, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 4, 4, 5, 5, 7, 3, 6, 4, 5, 3, 3, 4, 4, 4, 6, 3, 6, 3, 3, 4, 7, 5, 4, 7, 4, 4, 6, 6, 4, 8, 4, 5, 3, 3, 5, 5, 4, 4, 7, 4, 3, 5, 4, 6, 3, 4, 4, 8, 6, 3, 6, 5, 7, 3, 5, 5, 5, 4, 4, 4, 5, 3, 3, 3, 4, 6, 5, 6, 4, 8, 4, 5, 3, 3, 5, 5, 4, 3, 4, 3, 5, 3, 4, 3, 5, 5, 7, 6, 7, 3, 5, 4

Offset: 1

Author

Cino Hilliard, Sep 10 2004

Keywords

• easy
• nonn

Comments

Clearly sum of two consecutive primes prime(x) and prime(x+1) has more than 2 prime divisors for all x > 1.

Examples

			Prime(2) + prime(3) = 2*2*2, 3 factors, the second term in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071215, A251600 (greedy inverse).

Programs

Maple

A098037 := proc(n)
    ithprime(n)+ithprime(n+1) ;
    numtheory[bigomega](%) ;
end proc:
seq(A098037(n),n=1..40) ; # R. J. Mathar, Jan 20 2025

Mathematica

PrimeOmega[Total[#]]&/@Partition[Prime[Range[110]],2,1] (* Harvey P. Dale, Jun 14 2011 *)

PARI

b(n) = for(x=1,n,y1=(prime(x)+prime(x+1));print1(bigomega(y1)","))

Formula

a(n) = A001222(A001043(n)). - Michel Marcus, Feb 15 2014

Extensions

Definition corrected by Andrew S. Plewe, Apr 08 2007