A366972 - OEIS

%I #13 Oct 30 2023 11:12:56

%S 0,0,0,1,2,3,4,6,7,9,10,13,14,16,18,21,22,25,26,30,32,34,35,40,42,44,

%T 46,50,51,56,57,61,63,65,68,74,75,77,79,85,86,91,92,96,100,102,103,

%U 110,112,116,118,122,123,128,131,137,139,141,142,151,152,154,158,163,166

%N a(n) = Sum_{k=4..n} floor(n/k).

%F G.f.: 1/(1-x) * Sum_{k>=1} x^(4*k)/(1-x^k) = 1/(1-x) * Sum_{k>=4} x^k/(1-x^k).

%F a(n) = A006218(n)-n-floor(n/2)-floor(n/3). - _Chai Wah Wu_, Oct 30 2023

%o (PARI) a(n) = sum(k=4, n, n\k);

%o (Python)

%o from math import isqrt

%o def A366972(n): return -(s:=isqrt(n))**2+(sum(n//k for k in range(4,s+1))<<1)+n+(n>>1)+n//3 if n>8 else (0,0,0,0,1,2,3,4,6)[n] # _Chai Wah Wu_, Oct 30 2023

%Y Column k=4 of A134867.

%Y Partial sums of A321014.

%Y Cf. A006218.

%K nonn

%O 1,5

%A _Seiichi Manyama_, Oct 30 2023