cp's OEIS Frontend

A366983 a(n) = Sum_{k=1..n} (k+1) * floor(n/k).

%I A366983 #17 Oct 31 2023 21:57:21
%S A366983 2,7,13,23,31,47,57,76,92,114,128,162,178,206,234,270,290,335,357,405,
%T A366983 441,481,507,575,609,655,699,761,793,873,907,976,1028,1086,1138,1238,
%U A366983 1278,1342,1402,1500,1544,1648,1694,1784,1868,1944,1994,2128,2188,2287,2363,2467
%N A366983 a(n) = Sum_{k=1..n} (k+1) * floor(n/k).
%F A366983 a(n) = A006218(n) + A024916(n).
%F A366983 G.f.: 1/(1-x) * Sum_{k>0} (1/(1-x^k)^2 - 1) = 1/(1-x) * Sum_{k>0} (k+1) * x^k/(1-x^k).
%F A366983 a(n) = A257644(n) - 1. - _Hugo Pfoertner_, Oct 31 2023
%o A366983 (PARI) a(n) = sum(k=1, n, (k+1)*(n\k));
%o A366983 (Python)
%o A366983 from math import isqrt
%o A366983 def A366983(n): return -(s:=isqrt(n))*(s*(s+4)+5)+sum(((q:=n//w)+1)*(q+(w<<1)+4) for w in range(1,s+1))>>1 # _Chai Wah Wu_, Oct 31 2023
%Y A366983 Partial sums of A007503.
%Y A366983 Cf. A006218, A366984, A366985.
%Y A366983 Cf. A024916, A257644.
%K A366983 nonn,easy
%O A366983 1,1
%A A366983 _Seiichi Manyama_, Oct 30 2023