OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{k=1..n} a(k) ~ (n/(2*(zeta(2)-1))) * (log(n) + 3*gamma - 3 - 2*zeta'(2)/zeta(2) - log(1-1/zeta(2))), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 14 2024
EXAMPLE
MATHEMATICA
f[p_, e_] := p^Floor[e/2]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; s /@ Select[Range[300], !SquareFreeQ[#] &] (* Amiram Eldar, Feb 11 2021 *)
PROG
(Python)
from math import isqrt, prod
from sympy import mobius, factorint
def A087050(n):
def f(x): return n+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return prod(p**(e>>1) for p, e in factorint(m).items() if e>1) # Chai Wah Wu, Jul 22 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 08 2003
STATUS
approved