OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
FORMULA
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
MATHEMATICA
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]}]];
Array[a, 100] (* Jean-François Alcover, Nov 20 2020, after Max Alekseyev *)
PROG
(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
(Python)
from math import isqrt
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
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved