OFFSET
1,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
Henry Bottomley, Some Smarandache-type multiplicative sequences.
FORMULA
a(n) = n/A008835(n).
Dirichlet g.f.: zeta(4s)*zeta(s-1)/zeta(4s-4). The Dirichlet convolution of this sequence with A008835 is A000203. - R. J. Mathar, Apr 05 2011
From Peter Munn, Jan 15 2020: (Start)
a(2) = 2; a(4) = 4; a(n^4) = 1; a(A003961(n)) = A003961(a(n)); a(A059897(n,k)) = A059897(a(n), a(k)).
(End)
Multiplicative with a(p^e) = p^(e mod 4). - Amiram Eldar, Sep 07 2020
Sum_{k=1..n} a(k) ~ Pi^4 * n^2 / 210. - Vaclav Kotesovec, Aug 20 2021
MATHEMATICA
f[p_, e_] := p^Mod[e, 4]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 07 2020 *)
PROG
(Python)
from operator import mul
from functools import reduce
from sympy import factorint
def A053165(n):
return 1 if n <=1 else reduce(mul, [p**(e % 4) for p, e in factorint(n).items()])
# Chai Wah Wu, Feb 04 2015
(PARI) a(n)=my(f=factor(n)); f[, 2]=f[, 2]%4; factorback(f) \\ Charles R Greathouse IV, Sep 02 2015
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Henry Bottomley, Feb 29 2000
STATUS
approved