A137791 Number of ways to write n as sum of two positive numbers having no prime gaps in their factorization.

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 7, 8, 7, 7, 6, 8, 7, 8, 7, 8, 7, 9, 9, 10, 9, 10, 9, 11, 9, 11, 9, 10, 9, 11, 10, 10, 8, 10, 10, 13, 11, 12, 9, 11, 10, 14, 11, 12, 8, 10, 10, 14, 12, 13, 9, 12, 12, 14, 11, 12, 8, 11, 10, 16, 12, 11, 10, 14, 14, 16, 14, 14, 9, 13, 14, 18

Offset: 1

Author

Reinhard Zumkeller, Feb 11 2008

Keywords

• nonn

Examples

			a(20) = #{1+19,2+18,3+17,4+16,5+15,7+13,8+12,9+11} = 8;
a(21) = #{2+19,3+18,4+17,5+16,6+15,8+13,9+12} = 7;
a(22) = #{3+19,4+18,5+17,6+16,7+15,9+13,11+11} = 7;
a(23) = #{4+19,5+18,6+17,7+16,8+15,11+12} = 6;
a(24) = #{1+23,5+19,6+18,7+17,8+16,9+15,11+13,12+12} = 8.
		

Links

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

Crossrefs

Cf. A073491, A002375, A061358, A071330, A137792, A137793.