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A008835
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Largest 4th power dividing n.
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20
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 81
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OFFSET
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1,16
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LINKS
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FORMULA
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Multiplicative with a(p^e) = p^(4[e/4]). - Mitch Harris, Apr 19 2005
Dirichlet g.f.: zeta(s) * zeta(4s-4) / zeta(4s). - Álvar Ibeas, Feb 12 2015
Sum_{k=1..n} a(k) ~ zeta(5/4) * n^(5/4) / (5*zeta(5)) - 45*n/Pi^4. - Vaclav Kotesovec, Feb 03 2019
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MAPLE
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with(numtheory): [ seq( expand(nthpow(i, 4)), i=1..200) ];
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MATHEMATICA
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Max@ Select[Divisors@ #, IntegerQ@ Power[#, 1/4] &] & /@ Range@ 81 (* Michael De Vlieger, Mar 18 2015 *)
f[p_, e_] := p^(e - Mod[e, 4]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 15 2023 *)
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PROG
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(PARI) a(n) = {f = factor(n); for (i=1, #f~, f[i, 2] = 4*(f[i, 2]\4); ); factorback(f); } \\ Michel Marcus, Mar 16 2015
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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