

A053165


4thpowerfree part of n.


7



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
H. Bottomley, Some Smarandachetype multiplicative sequences


FORMULA

a(n) =n/A008835.
Dirichlet g.f. zeta(4s)*zeta(s1)/zeta(4s4). The Dirichlet convolution of this sequence with A008835 is A000203.  R. J. Mathar, Apr 05 2011


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

Cf. A000190, A007913, A008835, A050985.
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



