cp's OEIS Frontend

A366969 a(n) = Sum_{k=3..n} (k-2) * floor(n/k).

%I A366969 #16 Oct 31 2023 01:24:21
%S A366969 0,0,1,3,6,11,16,24,32,43,52,69,80,97,114,136,151,179,196,227,252,281,
%T A366969 302,347,373,408,441,486,513,570,599,651,692,739,780,854,889,942,991,
%U A366969 1066,1105,1186,1227,1300,1367,1432,1477,1582,1634,1716,1781,1868,1919,2024
%N A366969 a(n) = Sum_{k=3..n} (k-2) * floor(n/k).
%F A366969 G.f.: 1/(1-x) * Sum_{k>=1} x^(3*k)/(1-x^k)^2 = 1/(1-x) * Sum_{k>=3} (k-2) * x^k/(1-x^k).
%F A366969 a(n) = n + A024916(n) - 2*A006218(n). - _Chai Wah Wu_, Oct 30 2023
%o A366969 (PARI) a(n) = sum(k=3, n, (k-2)*(n\k));
%o A366969 (Python)
%o A366969 from math import isqrt
%o A366969 def A366969(n): return n+(-(s:=isqrt(n))*(s*(s-2)-7)+sum(((q:=n//w)+1)*(q+(w<<1)-8) for w in range(1,s+1))>>1) # _Chai Wah Wu_, Oct 30 2023
%Y A366969 Partial sums of A152771.
%Y A366969 Cf. A006218, A024916, A366968, A366970, A366971.
%K A366969 nonn
%O A366969 1,4
%A A366969 _Seiichi Manyama_, Oct 30 2023