A056160 Sum of A054988 and A054989.

1, 2, 2, 3, 2, 3, 5, 5, 5, 5, 3, 7, 4, 4, 6, 7, 6, 5, 5, 6, 4, 7, 5, 5, 5, 4, 8, 8, 7, 6, 8, 6, 9, 5, 6, 6, 9, 8, 9, 5, 11, 7, 9, 7, 9, 10, 11, 4, 9, 6, 7, 7, 7, 6, 8, 9, 8, 12, 7, 8, 8, 9, 7, 6, 8, 6, 9, 4, 8, 7, 12, 10, 7, 8, 7, 7, 10, 8, 9, 7, 9

Offset: 1

Author

Arne Ring (arne.ring(AT)epost.de), Aug 01 2000

Keywords

• hard
• nonn

Comments

Prime divisors are counted with multiplicity.

If "2" were a cluster point of this sequence it would follow that there are infinitely many twin primes.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..98

Crossrefs

Cf. A054988, A054989.

Programs

PARI

a(n) = my(P=prod(k=1, n, prime(k))); bigomega(P+1) + bigomega(P-1); \\ Michel Marcus, Mar 07 2022

Extensions

a(36)-a(81) from Charles R Greathouse IV, May 07 2011