OFFSET
1,16
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Henry Bottomley, Some Smarandache-type multiplicative sequences.
FORMULA
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
a(n) = A053164(n)^4. - Amiram Eldar, Sep 01 2024
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
(Python)
from math import prod
from sympy import factorint
def A008835(n): return prod(p**(e&-4) for p, e in factorint(n).items()) # Chai Wah Wu, Aug 08 2024
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
EXTENSIONS
Entry improved by comments from Henry Bottomley, Feb 29 2000
STATUS
approved