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A132741
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Largest divisor of n having the form 2^i*5^j.
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7
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1, 2, 1, 4, 5, 2, 1, 8, 1, 10, 1, 4, 1, 2, 5, 16, 1, 2, 1, 20, 1, 2, 1, 8, 25, 2, 1, 4, 1, 10, 1, 32, 1, 2, 5, 4, 1, 2, 1, 40, 1, 2, 1, 4, 5, 2, 1, 16, 1, 50, 1, 4, 1, 2, 5, 8, 1, 2, 1, 20, 1, 2, 1, 64, 5, 2, 1, 4, 1, 10, 1, 8, 1, 2, 25, 4, 1, 2, 1, 80, 1, 2, 1, 4, 5, 2, 1, 8, 1, 10, 1, 4, 1, 2, 5, 32, 1, 2
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OFFSET
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1,2
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COMMENTS
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The range of this sequence, { a(n); n>=0 }, is equal to A003592. - M. F. Hasler, Dec 28 2015
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = n / A132740(n).
a(A003592(n)) = A003592(n).
A051626(a(n)) = 0.
A007732(a(n)) = 1.
From R. J. Mathar, Sep 06 2011: (Start)
Multiplicative with a(2^e)=2^e, a(5^e)=5^e and a(p^e)=1 for p=3 or p>=7.
Dirichlet g.f. zeta(s)*(2^s-1)*(5^s-1)/((2^s-2)*(5^s-5)). (End)
a(n) = A006519(n)*A060904(n) = 2^A007814(n)*5^A112765(n). - M. F. Hasler, Dec 28 2015
Sum_{k=1..n} a(k) ~ n*(12*log(n)^2 + (24*gamma + 36*log(2) - 24)*log(n) + 24 - 24*gamma - 36*log(2) + 36*gamma*log(2) + 2*log(2)^2 - 18*log(5) + 18*gamma*log(5) + 27*log(2)*log(5) + 2*log(5)^2 + 18*log(5)*log(n) - 24*gamma_1)/(60*log(2)*log(5)), gamma is the Euler's constant (A001620) and gamma_1 is the first Stieltjes constant (A082633). - Amiram Eldar, Jan 26 2023
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MAPLE
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A132741 := proc(n) local f, a; f := ifactors(n)[2] ; a := 1; for f in ifactors(n)[2] do if op(1, f) =2 then a := a*2^op(2, f) ; elif op(1, f) =5 then a := a*5^op(2, f) ; end if; end do; a; end proc: # R. J. Mathar, Sep 06 2011
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MATHEMATICA
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a[n_] := SelectFirst[Reverse[Divisors[n]], MatchQ[FactorInteger[#], {{1, 1}} | {{2, _}} | {{5, _}} | {{2, _}, {5, _}}]&]; Array[a, 100] (* Jean-François Alcover, Feb 02 2018 *)
a[n_] := Times @@ ({2, 5}^IntegerExponent[n, {2, 5}]); Array[a, 100] (* Amiram Eldar, Jun 12 2022 *)
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PROG
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(Haskell)
a132741 = f 2 1 where
f p y x | r == 0 = f p (y * p) x'
| otherwise = if p == 2 then f 5 y x else y
where (x', r) = divMod x p
-- Reinhard Zumkeller, Nov 19 2015
(PARI) A132741(n)=5^valuation(n, 5)<<valuation(n, 2) \\ M. F. Hasler, Dec 28 2015
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CROSSREFS
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Cf. A003592, A006519, A007732, A007814, A051626, A060904, A112765, A132740.
Cf. A001620, A082633.
Sequence in context: A248666 A162407 A352458 * A072436 A247503 A343430
Adjacent sequences: A132738 A132739 A132740 * A132742 A132743 A132744
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KEYWORD
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nonn,easy,mult
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AUTHOR
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Reinhard Zumkeller, Aug 27 2007
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STATUS
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approved
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