OFFSET
1,2
COMMENTS
For more information about the quarter-squares see A002620.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Wikipedia, Table of divisors.
FORMULA
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = zeta(2) + 1 = A013661 + 1 = 2.644934... . - Amiram Eldar, Dec 31 2023
EXAMPLE
For n = 12 the quarter-squares <= 12 are [0, 0, 1, 2, 4, 6, 9, 12]. There are five quarter-squares that divide 12; they are [1, 2, 4, 6, 12], so a(12) = 5.
MAPLE
isA002620 := proc(n)
local k, qsq ;
for k from 0 do
qsq := floor(k^2/4) ;
if n = qsq then
return true;
elif qsq > n then
return false;
end if;
end do:
end proc:
A239930 := proc(n)
local a, d ;
a :=0 ;
for d in numtheory[divisors](n) do
if isA002620(d) then
a:= a+1 ;
end if;
end do:
a;
end proc: # R. J. Mathar, Jul 03 2014
MATHEMATICA
qsQ[n_] := AnyTrue[Range[Ceiling[2 Sqrt[n]]], n == Floor[#^2/4]&]; a[n_] := DivisorSum[n, Boole[qsQ[#]]&]; Array[a, 110] (* Jean-François Alcover, Feb 12 2018 *)
PROG
(Haskell)
a239930 = sum . map a240025 . a027750_row
-- Reinhard Zumkeller, Jul 05 2014
(PARI) a(n) = sumdiv(n, d, issquare(d) + issquare(4*d + 1)); \\ Amiram Eldar, Dec 31 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jun 19 2014
STATUS
approved