OFFSET
1,6
COMMENTS
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{k=1..n} a(k) ~ n*log(n) + (2*gamma - zeta(2) - 1)*n, where gamma is Euler's constant (A001620). - Amiram Eldar, Dec 01 2023
EXAMPLE
a(36)=5 because the set of divisors of 36 has tau(36)=nine elements, {1, 2, 3, 4, 6, 9, 12, 18, 36}, five of which, that is {2, 3, 6, 12, 18}, are not perfect squares.
MAPLE
A056595 := proc(n)
local a, d ;
a := 0 ;
for d in numtheory[divisors](n) do
if not issqr(d) then
a := a+1 ;
end if;
end do:
a;
end proc:
seq(A056595(n), n=1..40) ; # R. J. Mathar, Aug 18 2024
MATHEMATICA
Table[Count[Divisors[n], _?(#!=Floor[Sqrt[#]]^2&)], {n, 110}] (* Harvey P. Dale, Jul 10 2013 *)
a[1] = 0; a[n_] := Times @@ (1 + (e = Last /@ FactorInteger[n])) - Times @@ (1 + Floor[e/2]); Array[a, 100] (* Amiram Eldar, Jul 22 2019 *)
PROG
(Haskell)
a056595 n = length [d | d <- [1..n], mod n d == 0, a010052 d == 0]
-- Reinhard Zumkeller, Aug 15 2011
(PARI) a(n)=sumdiv(n, d, !issquare(d)) \\ Charles R Greathouse IV, Aug 28 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 21 2000
STATUS
approved