A350996 a(n) = Sum_{k=1..n} k * rad(k).

1, 5, 14, 22, 47, 83, 132, 148, 175, 275, 396, 468, 637, 833, 1058, 1090, 1379, 1487, 1848, 2048, 2489, 2973, 3502, 3646, 3771, 4447, 4528, 4920, 5761, 6661, 7622, 7686, 8775, 9931, 11156, 11372, 12741, 14185, 15706, 16106, 17787, 19551, 21400, 22368, 23043, 25159

Offset: 1

Author

Wesley Ivan Hurt, Jan 28 2022

Keywords

• nonn

Examples

			a(4) = 22; a(4) = Sum_{k=1..4} k * rad(k) = 1*rad(1) + 2*rad(2) + 3*rad(3) + 4*rad(4) = 1*1 + 2*2 + 3*3 + 4*2 = 22.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Wikipedia, Radical of an integer.

Crossrefs

Cf. A007947 (rad), A073355, A064549, A065463.

Programs

Mathematica

f[n_] := n * Times @@ FactorInteger[n][[;; , 1]]; Accumulate @ Array[f, 50] (* Amiram Eldar, Jan 29 2022 *)

PARI

a(n) = sum(k=1, n, k*factorback(factorint(k)[, 1])); \\ Michel Marcus, Jan 30 2022

Formula

a(n) = Sum_{k=1..n} A064549(k).

a(n) ~ c * n^3 / 3, where c = A065463. - Amiram Eldar, Dec 09 2023