OFFSET
1,4
COMMENTS
The Dirichlet generating function of the arithmetic function of the largest t-th power dividing n is zeta(s)*zeta(t*s-t)/zeta(s*t), here with t=2 and in A008834 and A008835 with t=3 and t=4, respectively. - R. J. Mathar, Feb 19 2011
LINKS
Daniel Forgues, Table of n, a(n) for n = 1..100000
Henry Bottomley, Some Smarandache-type multiplicative sequences
R. J. Mathar, Survey of Dirichlet series of multiplicative arithmetic functions arXiv:1106.4038 [math.NT], 2011-2012, Remark 16.
Andrew Reiter, On (mod n) spirals, 2014, see also posting to Number Theory Mailing List, Mar 23 2014.
Eric Weisstein's World of Mathematics, Square part
FORMULA
Multiplicative with a(p^e) = p^(2[e/2]). - David W. Wilson, Aug 01 2001
Dirichlet g.f.: zeta(s)*zeta(2s-2)/zeta(2s). - R. J. Mathar, Oct 31 2011
Sum_{k=1..n} a(k) ~ Zeta(3/2) * n^(3/2) / (3*Zeta(3)). - Vaclav Kotesovec, Feb 01 2019
MATHEMATICA
a[n_] := First[ Select[ Reverse[ Divisors[n]], IntegerQ[Sqrt[#]]&, 1]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Dec 12 2011 *)
f[p_, e_] := p^(2*Floor[e/2]); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Jul 07 2020 *)
PROG
(PARI) A008833(n)=n/core(n) \\ Michael B. Porter, Oct 17 2009
(Haskell)
a008833 n = head $ filter ((== 0) . (mod n)) $
reverse $ takeWhile (<= n) $ tail a000290_list
-- Reinhard Zumkeller, Nov 13 2011
(Python)
from sympy.ntheory.factor_ import core
def A008833(n): return n//core(n) # Chai Wah Wu, Dec 30 2021
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
STATUS
approved