A088627 - OEIS

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

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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