

A162947


Numbers n such that the product of all divisors of n equals n^3.


3



1, 12, 18, 20, 28, 32, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99, 116, 117, 124, 147, 148, 153, 164, 171, 172, 175, 188, 207, 212, 236, 242, 243, 244, 245, 261, 268, 275, 279, 284, 292, 316, 325, 332, 333, 338, 356, 363, 369, 387, 388, 404, 412, 423, 425, 428
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OFFSET

1,2


COMMENTS

Contains the terms of A054753 (products p*q^2 of a prime p and a different prime q), 1, and p^5, where p is prime.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


FORMULA

{n: A007955(n) = A000578(n)}. R. J. Mathar, Jul 19 2009
{1} UNION A030515.  R. J. Mathar, Jul 19 2009
n such that n^2 = product of proper divisors of n.  JuriStepan Gerasimov, May 03 2011.


EXAMPLE

18 is in the sequence because the product of its divisors is 1 * 2 * 3 * 6 * 9 * 18 = 18^3.


MATHEMATICA

Select[Range[500], Surd[Times@@Divisors[#], 3] == # &] (* Harvey P. Dale, Mar 15 2017 *)


PROG

(PARI) isok(n) = my(d = divisors(n)); prod(i=1, #d, d[i]) == n^3; \\ Michel Marcus, Feb 04 2014


CROSSREFS

Cf. A111398, A030628.  R. J. Mathar, Jul 19 2009
Cf. A008578 (product of divisors equals n), A007422 (product of divisors equals n^2).
Sequence in context: A217856 A253388 A030515 * A070011 A084679 A072588
Adjacent sequences: A162944 A162945 A162946 * A162948 A162949 A162950


KEYWORD

nonn


AUTHOR

Claudio Meller, Jul 18 2009


EXTENSIONS

Edited by R. J. Mathar, Jul 19 2009


STATUS

approved



