|
%I #24 Oct 31 2023 12:32:49
%S 1,3,4,7,8,12,13,15,19,21,22,28,29,31,33,39,40,43,44,51,53,55,56,60,
%T 66,68,70,73,74,83,84,87,89,91,93,103,104,106,108,112,113,123,124,127,
%U 130,132,133,138,146,149,151,154,155,159,161,172,174,176,177,183,184,186
%N Sum of elements of the set { [ n/k ] : 1 <= k <= n }.
%H Alois P. Heinz, <a href="/A051201/b051201.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = m*(m+1)/2 + Sum_{k=1..floor(n/(m+1))} floor(n/k), where m is the largest number such that m*(m+1) <= n, i.e., m=floor( (sqrt(4*n+1)-1)/2 ). - _Max Alekseyev_, Feb 12 2012
%t a[n_] := With[{m = Quotient[Floor@Sqrt[4n+1]-1, 2]}, m(m+1)/2 + Sum[ Quotient[n, k], {k, 1, Quotient[n, m+1]}]];
%t Array[a, 100] (* _Jean-François Alcover_, Nov 20 2020, after _Max Alekseyev_ *)
%o (PARI) { a(n) = m=(sqrtint(4*n+1)-1)\2; m*(m+1)/2 + sum(k=1,n\(m+1),n\k) } \\ _Max Alekseyev_, Feb 12 2012
%o (Python)
%o from math import isqrt
%o def A051201(n): return ((m:=isqrt((n<<2)+1)+1>>1)*(m-1)>>1)+sum(n//k for k in range(1,n//m+1)) # _Chai Wah Wu_, Oct 31 2023
%Y Cf. A006218.
%K nonn
%O 1,2
%A _David W. Wilson_
|
