A088627 Let 2n = r*s. Then a(n) = number of primes of the form r+s (r= 1 and s = 2n contributes 1 to the count if 2n+1 is prime).

1, 1, 2, 0, 2, 2, 0, 1, 2, 0, 2, 1, 0, 2, 4, 0, 1, 2, 0, 2, 4, 0, 1, 1, 0, 2, 1, 0, 2, 4, 0, 0, 2, 0, 4, 2, 0, 1, 4, 0, 2, 2, 0, 2, 3, 0, 0, 1, 0, 2, 4, 0, 1, 2, 0, 2, 2, 0, 1, 3, 0, 0, 2, 0, 4, 3, 0, 1, 3, 0, 1, 0, 0, 2, 3, 0, 2, 2, 0, 1, 2, 0, 1, 3, 0, 2, 2, 0, 1, 3, 0, 1, 1, 0, 4, 2, 0, 2, 4, 0, 1, 2, 0, 1, 8

Offset

1,3

Comments

Only even numbers yield primes hence odd numbers are not considered.

There is an upper bound: if n has only k different prime divisors > 2, then a(n) <= 2^k. - Matthias Engelhardt, Jan 05 2004

Links

T. D. Noe, Table of n, a(n) for n=1..10000

M. Engelhardt, Number of Primes arising as Sum of a Factorization.

Example

a(9) = 2 18 = 1*18, 1+18= 19 and 18 = 2*9, 2+9 = 11, two primes arise.

Crossrefs

Cf. A091350.

Sequence in context: A164273 A307694 A106277 * A230205 A334841 A024713

Adjacent sequences: A088624 A088625 A088626 * A088628 A088629 A088630

Keyword

nonn

Author

Amarnath Murthy, Oct 19 2003

Extensions

More terms from Matthias Engelhardt, Jan 05 2004

More terms from David Wasserman, Aug 15 2005

Status

approved