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A053165 4th-power-free 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 Smarandache-type multiplicative sequences

FORMULA

a(n) =n/A008835.

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

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

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Last modified December 3 08:48 EST 2016. Contains 278698 sequences.