A063648 Smallest c such that 1/n=1/c+1/b has integer solutions with c>b.

6, 12, 12, 30, 15, 56, 24, 36, 30, 132, 28, 182, 42, 40, 48, 306, 45, 380, 45, 70, 66, 552, 56, 150, 78, 108, 77, 870, 66, 992, 96, 132, 102, 84, 84, 1406, 114, 156, 90, 1722, 91, 1892, 132, 120, 138, 2256, 112, 392, 150, 204, 156, 2862, 135, 176, 120, 228, 174

Offset: 2

Author

Henry Bottomley, Jul 23 2001

Keywords

• nonn

Comments

Largest c is n(n+1) since 1/n=1/(n(n+1))+1/(n+1)

Examples

			a(10)=30 since 1/10=1/20+1/20=1/30+1/15=1/35+1/14=1/60+1/12=1/110+1/11, but the first sum does not have c>b, leaving the second sum to provide the value.
		

Crossrefs

Cf. A018892, A063427, A063428, A063647, A063649.

Formula

a(n) =n*A063649(n)/(A063649(n)-n) =A063427(n)+2n.