A227043 Numerator of harmonic mean H(n,2), n>= 0.

0, 4, 2, 12, 8, 20, 3, 28, 16, 36, 10, 44, 24, 52, 7, 60, 32, 68, 18, 76, 40, 84, 11, 92, 48, 100, 26, 108, 56, 116, 15, 124, 64, 132, 34, 140, 72, 148, 19, 156, 80, 164, 42, 172, 88, 180, 23, 188, 96, 196, 50, 204, 104, 212, 27, 220, 112, 228, 58, 236, 120

Offset: 0

Author

Wolfdieter Lang, Jul 01 2013

Keywords

• nonn
• easy
• frac

Comments

a(n) = numerator(H(n,2)) = numerator(4*n/(n+2)), n>=0, with H(n,2) the harmonic mean of n and 2.

The corresponding denominator is given in A000265(n+2), n>= 0.

a(n+2), n>=0, is the second column (m=2) of the triangle A227041.

Examples

			The rationals H(n,2) begin:
0, 4/3, 2, 12/5, 8/3, 20/7, 3, 28/9, 16/5, 36/11, 10/3, 44/13, 24/7, 52/15, 7/2, 60/17, ...
		

Crossrefs

Cf. A227041(n+2,2), A000265(n+2) (denominator), n >= 0.

Formula

a(n) = numerator(4*n/(n+2)), n >= 0.

a(n) = 4*n/gcd(n+2,4*n) = 4*n/gcd(n+2,8), n >= 0.