login
a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/k)^3).
3

%I #20 Oct 27 2023 21:17:01

%S 1,7,25,57,114,194,310,460,658,902,1200,1557,1981,2474,3045,3690,4431,

%T 5257,6186,7212,8350,9601,10969,12461,14088,15844,17746,19791,21990,

%U 24343,26859,29539,32399,35434,38655,42060,45671,49468,53480,57698,62137,66793,71681

%N a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/k)^3).

%F a(n) = A309082(n^3).

%t a[n_] := Sum[(-1)^(k + 1)*Floor[(n/k)^3], {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, Dec 20 2021 *)

%o (PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n^3\k^3));

%o (Python)

%o def A350222(n): return (m:=n**3)+sum(m//k**3 if k&1 else -(m//k**3) for k in range(2,n+1)) # _Chai Wah Wu_, Oct 27 2023

%Y Cf. A000578, A309082, A344675, A344721, A350221, A350224.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Dec 20 2021