A350996 - OEIS

%I #18 Dec 09 2023 07:08:08

%S 1,5,14,22,47,83,132,148,175,275,396,468,637,833,1058,1090,1379,1487,

%T 1848,2048,2489,2973,3502,3646,3771,4447,4528,4920,5761,6661,7622,

%U 7686,8775,9931,11156,11372,12741,14185,15706,16106,17787,19551,21400,22368,23043,25159

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

%H Amiram Eldar, <a href="/A350996/b350996.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Radical_of_an_integer">Radical of an integer</a>.

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

%F a(n) ~ c * n^3 / 3, where c = A065463. - _Amiram Eldar_, Dec 09 2023

%e 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.

%t f[n_] := n * Times @@ FactorInteger[n][[;; , 1]]; Accumulate @ Array[f, 50] (* _Amiram Eldar_, Jan 29 2022 *)

%o (PARI) a(n) = sum(k=1, n, k*factorback(factorint(k)[, 1])); \\ _Michel Marcus_, Jan 30 2022

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

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jan 28 2022