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A008835 Largest 4th power dividing n. 20
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,16
LINKS
FORMULA
a(n) = A000188(A000188(n))^4.
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
a(n) = n/A053165(n). - Amiram Eldar, Aug 15 2023
MAPLE
with(numtheory): [ seq( expand(nthpow(i, 4)), i=1..200) ];
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A265491 A209201 A050467 * A040259 A353806 A040260
KEYWORD
nonn,easy,mult
AUTHOR
EXTENSIONS
Entry improved by comments from Henry Bottomley, Feb 29 2000
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)