A061297 a(n) = Sum_{ r = 0 to n} L(n,r), where L(n,r) (A067049) = lcm(n, n-1, n-2, ..., n-r+1)/lcm(1, 2, 3, ..., r).

1, 2, 4, 8, 14, 32, 39, 114, 166, 266, 421, 1608, 1005, 3980, 6894, 4206, 8666, 40904, 49559, 315478, 162321, 79180, 269878, 1647124, 937553, 1810092, 8445654, 7791356, 3978238, 33071544, 19578861, 283536170, 327438714, 117635956, 742042967, 154748984, 88779589, 1532487536, 10514107742, 3761632498

Offset: 0

Author

Amarnath Murthy, Apr 26 2001

Keywords

• nonn
• easy

Comments

The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975. - Jeremy Gardiner, Dec 28 2008

Examples

			a(0) = 1, a(4) = 14: we have L(4,0) = 1, L(4,1) = 4, L(4,2) = 6, L(4,3) = 2, L(4,4) = 1. For r = 0 to 4, sigma {L(4,r)}= 1 + 4 + 6 + 2 + 1 = 14.
		

References

• Amarnath Murthy, Some Notions On Least Common Multiples, Smarandache Notions Journal, Vol. 12, No. 1-2-3, Spring 2001.

Links

• Tanya Khovanova, There are no coincidences, arXiv preprint 1410.2193 [math.CO], 2014.

Crossrefs

Row sums of A067049.

Programs

PARI

tlcm(n, r) = {nt = 1; for (k = n-r+1, n, nt = lcm(nt, k);); dt = 1; for (k = 1, r, dt = lcm(dt, k);); return (nt/dt);}
a(n) = sum(r = 0, n , tlcm(n, r)); \\ Michel Marcus, Sep 14 2013