%I #17 Oct 31 2023 21:57:21

%S 2,7,13,23,31,47,57,76,92,114,128,162,178,206,234,270,290,335,357,405,

%T 441,481,507,575,609,655,699,761,793,873,907,976,1028,1086,1138,1238,

%U 1278,1342,1402,1500,1544,1648,1694,1784,1868,1944,1994,2128,2188,2287,2363,2467

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

%F a(n) = A006218(n) + A024916(n).

%F 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 a(n) = A257644(n) - 1. - _Hugo Pfoertner_, Oct 31 2023

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

%o (Python)

%o from math import isqrt

%o 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 Partial sums of A007503.

%Y Cf. A006218, A366984, A366985.

%Y Cf. A024916, A257644.

%K nonn,easy

%O 1,1

%A _Seiichi Manyama_, Oct 30 2023