A344460 a(n) = Sum_{d|n} d * floor(sqrt(d)).

1, 3, 4, 11, 11, 18, 15, 27, 31, 43, 34, 62, 40, 59, 59, 91, 69, 117, 77, 131, 102, 124, 93, 174, 136, 172, 166, 207, 146, 253, 156, 251, 202, 241, 200, 377, 223, 307, 277, 387, 247, 410, 259, 396, 356, 371, 283, 526, 358, 518, 429, 544, 372, 630, 429, 615, 479, 554, 414, 797

Offset: 1

Author

Wesley Ivan Hurt, May 19 2021

Keywords

• nonn

Comments

Inverse Möbius transform of n * floor(sqrt(n)). - Wesley Ivan Hurt, Mar 31 2025

Examples

			a(10) = Sum_{d|10} d * floor(sqrt(d)) = 1*1 + 2*1 + 5*2 + 10*3 = 43.
		

Crossrefs

Cf. A000196, A086671.

Programs

Mathematica

Table[Sum[k*Floor[Sqrt[k]] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]