A344405 a(n) = Sum_{d|n} (n/d) * floor(n/d^2).

1, 4, 9, 18, 25, 39, 49, 72, 84, 110, 121, 166, 169, 217, 230, 292, 289, 372, 361, 455, 455, 539, 529, 670, 630, 754, 756, 889, 841, 1041, 961, 1168, 1122, 1292, 1232, 1530, 1369, 1615, 1573, 1828, 1681, 2037, 1849, 2200, 2109, 2369, 2209, 2716, 2408, 2820, 2686

Offset: 1

Author

Wesley Ivan Hurt, May 16 2021

Keywords

• nonn

Comments

If p is prime, a(p) = Sum_{d|p} (p/d) * floor(p/d^2) = p*p + 1*0 = p^2.

Examples

			a(4) = 18; Sum_{d|4} (4/d) * floor(4/d^2) = 4*4 + 2*1 + 1*0 = 18.
		

Crossrefs

Cf. A344128, A344403, A344404.

Programs

Mathematica

Table[Sum[(1 - Ceiling[n/k] + Floor[n/k]) (n/k) Floor[n/k^2], {k, n}], {n, 100}]

PARI

a(n) = sumdiv(n, d, (n/d)*(n\d^2)); \\ Michel Marcus, May 17 2021