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 A008833 Largest square dividing n. 87
 1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 4, 1, 1, 1, 16, 1, 9, 1, 4, 1, 1, 1, 4, 25, 1, 9, 4, 1, 1, 1, 16, 1, 1, 1, 36, 1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 16, 49, 25, 1, 4, 1, 9, 1, 4, 1, 1, 1, 4, 1, 1, 9, 64, 1, 1, 1, 4, 1, 1, 1, 36, 1, 1, 25, 4, 1, 1, 1, 16, 81, 1, 1, 4, 1, 1, 1, 4, 1, 9, 1, 4, 1, 1, 1, 16, 1 (list; graph; refs; listen; history; text; internal format)
 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 a(n) = A000188(n)^2 = n/A007913(n). Cf. A019554. 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 a(n) = A005563(n-1) / A068310(n) for n > 1. - Reinhard Zumkeller, Nov 26 2011 Sum_{k=1..n} a(k) ~ Zeta(3/2) * n^(3/2) / (3*Zeta(3)). - Vaclav Kotesovec, Feb 01 2019 a(A059897(n,k)) = A059897(a(n), a(k)). - Peter Munn, Nov 30 2019 MAPLE A008833 := proc(n) expand(numtheory:-nthpow(n, 2)) ; end proc: seq(A008833(n), n=1..100) ; 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 Cf. A000188, A005563, A007913, A019554, A059897, A068310. Sequence in context: A350698 A335324 A083730 * A162400 A332012 A179054 Adjacent sequences: A008830 A008831 A008832 * A008834 A008835 A008836 KEYWORD nonn,easy,mult AUTHOR STATUS approved

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Last modified December 5 20:49 EST 2022. Contains 358593 sequences. (Running on oeis4.)