OFFSET
0,6
COMMENTS
Number of partitions of n into 3 parts such that the smallest part divides the "middle" part. - Wesley Ivan Hurt, Oct 21 2021
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = Sum_{j=1..n} A069283(j).
a(n) = A060831(n) - n.
a(n) = Sum_{i=1..n-1} floor(floor(i/2)/(n-i)). - Wesley Ivan Hurt, Jan 30 2016
MATHEMATICA
Table[Sum[Floor[Floor[i/2]/(n - i)], {i, n - 1}], {n, 0, 100}] (* Wesley Ivan Hurt, Jan 30 2016 *)
Join[{0}, Accumulate[Table[Count[Divisors[n], _?OddQ]-1, {n, 80}]]] (* Harvey P. Dale, Jan 06 2019 *)
Join[{0}, Accumulate[Table[DivisorSigma[0, n/2^IntegerExponent[n, 2]] - 1, {n, 1, 100}]]] (* Amiram Eldar, Jul 10 2022 *)
PROG
(PARI) a(n)=my(n2=n\2); sum(k=1, sqrtint(n), n\k)*2-sqrtint(n)^2-sum(k=1, sqrtint(n2), n2\k)*2+sqrtint(n2)^2-n \\ Charles R Greathouse IV, Jun 18 2015
(Python)
from math import isqrt
def A248517(n): return ((t:=isqrt(m:=n>>1))+(s:=isqrt(n)))*(t-s)+(sum(n//k for k in range(1, s+1))-sum(m//k for k in range(1, t+1))<<1)-n # Chai Wah Wu, Oct 23 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Jun 18 2015
STATUS
approved