A333354 Minimum cost of path that starts at 1 and visits integers from 1 to n, inclusive, each at least once, where the cost to travel from a to b is LCM(a, b).

0, 2, 7, 12, 21, 28, 40, 51, 65, 79, 100, 114, 138, 158, 182, 205, 238, 259, 295, 324, 358, 390, 435, 463, 511, 549, 593, 634

Offset: 1

Author

Richard S. Chang, May 04 2020

Keywords

• nonn
• hard
• more

Examples

			For n = 3, the optimal path is 1, 2, 1, 3, which has cost 2 + 2 + 3 = 7.
For n = 4, the optimal path is 1, 3, 1, 2, 4, which has cost 3 + 3 + 2 + 4 = 12.
For n = 7, there are multiple optimal paths of which 1, 3, 6, 2, 4, 1, 5, 1, 7 is one and has cost 3 + 6 + 6 + 4 + 4 + 5 + 5 + 7 = 40.
For n = 20, an optimal path is 1, 11, 1, 13, 1, 17, 1, 19, 1, 7, 14, 2, 16, 8, 4, 12, 6, 18, 9, 3, 15, 5, 10, 20.
		

Links

• A. Catanzaro, J. Feldman, M. Higgins, B. Kimball, H. Kirk, A. C Maravelias, and D. Sinha, LCM Optimal Paths, Girls' Angle Bulletin, Vol. 13, No. 4 (2020), 13-19.

Extensions

a(21)-a(28) from Bert Dobbelaere, Aug 22 2020