A100951 Number of ways to write n = p*q + r with three distinct primes p, q and r.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 4, 0, 2, 0, 1, 1, 3, 0, 3, 2, 3, 1, 4, 0, 2, 2, 3, 2, 3, 0, 5, 4, 3, 2, 5, 0, 4, 3, 5, 4, 3, 1, 4, 3, 5, 4, 6, 1, 3, 4, 6, 6, 4, 0, 3, 7, 6, 5, 6, 1, 6, 6, 6, 4, 4, 3, 4, 7, 7, 6, 6, 2, 6, 7, 8, 8, 3, 2, 7, 6, 7, 8, 8, 1, 4, 7, 10, 10, 6, 6, 7, 10, 9, 8, 5, 5, 5, 8

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2004

Keywords

• nonn

Comments

a(n)<=A100950(n)<=A100949(n)<=Min{A000720(n), A072000(n)}.

a(n) = A000040(i) + A006881(j) for some i and j, such that A000040(i) is not a factor of A006881(j);

a(A100952(n)) = 0.

a(A160373(n)) = n and a(m) <> n for m < A160373(n). [From Reinhard Zumkeller, May 11 2009]

Examples

			A100949(21) = #{7+2*7, 11+2*5, 17+2*2} = 3,
a(21) = #{11+2*5} = 1.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 1..10000