login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053165 4th-power-free part of n. 11
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 2, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 3, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 4, 65, 66, 67, 68, 69, 70, 71, 72, 73 (list; graph; refs; listen; history; text; internal format)
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)).

a(A225546(n)) = A225546(A065331(n)).

(End)

Multiplicative with a(p^e) = p^(e mod 4). - Amiram Eldar, Sep 07 2020

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

Equivalent sequences for other powers: A007913 (2), A050985 (3).

Cf. A000190, A000203, A008835.

A003961, A059897 are used to express relationship between terms of this sequence.

Related to A065331 via A225546.

Sequence in context: A002377 A053836 A025483 * A056962 A043275 A216455

Adjacent sequences:  A053162 A053163 A053164 * A053166 A053167 A053168

KEYWORD

nonn,mult

AUTHOR

Henry Bottomley, Feb 29 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 23 21:27 EDT 2020. Contains 337315 sequences. (Running on oeis4.)