A121611 Number of ways to express n as an average of three distinct primes.

0, 0, 0, 1, 1, 2, 2, 2, 3, 2, 4, 3, 6, 3, 6, 3, 8, 3, 10, 3, 12, 5, 13, 5, 14, 5, 17, 4, 21, 4, 22, 4, 21, 6, 23, 5, 27, 7, 32, 5, 36, 5, 35, 7, 34, 5, 36, 7, 43, 5, 46, 8, 47, 8, 44, 5, 52, 6, 55, 6, 61, 8, 58, 8, 57, 9, 67, 8, 71, 7, 79, 7, 72, 9, 69, 6, 76, 7, 83, 9, 94, 9, 91, 9, 89, 8, 94, 8

Offset: 1

Author

Zak Seidov, Sep 08 2006

Keywords

• nonn

Comments

For odd n's a(n) are much larger than a(n-/+1). Cf. A061357 = number of ways n can be expressed as the mean of two distinct primes, A061357 = number of ways the even integer 2n can be written as the sum of two primes for all even integers >6.

Examples

			a(4)=1 because 4 = (2+3+7)/3 (1 way),
a(6)=2 because 6 = (2+3+13)/3 = (2+5+11)/3 (2 ways)
a(9)=3 because 9 = (3+5+19)/3 = (3+7+17)/3 = (3+11+13)/3 (3 ways)
a(11)=4 because 11 = (3+7+23)/3 = (3+11+19)/3 = (3+13+17)/3 = (5+11+19)/3 (4 ways), etc.
		

Crossrefs

Cf. A061357, A061357.