A345304 a(n) = Sum_{p|n, p prime} p * lcm(p,n/p).

0, 4, 9, 4, 25, 30, 49, 8, 9, 70, 121, 48, 169, 126, 120, 16, 289, 54, 361, 120, 210, 286, 529, 96, 25, 390, 27, 224, 841, 300, 961, 32, 462, 646, 420, 72, 1369, 798, 624, 240, 1681, 504, 1849, 528, 270, 1150, 2209, 192, 49, 150, 1020, 728, 2809, 162, 880, 448, 1254, 1798, 3481

Offset: 1

Author

Wesley Ivan Hurt, Jun 13 2021

Keywords

• nonn

Comments

If p is prime, a(p) = Sum_{p|p} p * lcm(p,p/p) = p * p = p^2.

Examples

			a(18) = Sum_{p|18} p * lcm(p,18/p) = 2*lcm(2,9) + 3*lcm(3,6) = 2*18 + 3*6 = 54.
		

Links

• Index entries for sequences related to lcm's

Crossrefs

Cf. A008472, A345266, A345302.

Programs

Mathematica

Table[Sum[k*LCM[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]