

A019555


Smallest number whose cube is divisible by n.


13



1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, 19, 10, 21, 22, 23, 6, 5, 26, 3, 14, 29, 30, 31, 4, 33, 34, 35, 6, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 12, 7, 10, 51, 26, 53, 6, 55, 14, 57, 58, 59, 30, 61, 62, 21, 4, 65, 66, 67, 34, 69, 70, 71, 6, 73, 74, 15, 38, 77, 78
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OFFSET

1,2


COMMENTS

This can be thought as an "upper 3rd root" of a positive integer. Upper kth roots were studied by Broughan (2002, 2003, 2006). The sequence of "lower 3rd root" of positive integers is given by A053150.  Petros Hadjicostas, Sep 15 2019


LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000
H. Bottomley, Some Smarandachetype multiplicative sequences.
Kevin A. Broughan, Restricted divisor sums, Acta Arithmetica, 101(2) (2002), 105114.
Kevin A. Broughan, Relationship between the integer conductor and kth root functions, Int. J. Pure Appl. Math. 5(3) (2003), 253275.
Kevin A. Broughan, Relaxations of the ABC Conjecture using integer k'th roots, New Zealand J. Math. 35(2) (2006), 121136.
F. Smarandache, Collected Papers, Vol. II, Tempus Publ. Hse, Bucharest, 1996.
Eric Weisstein's World of Mathematics, Smarandache Ceil Function.


FORMULA

Replace any cubic factors in n by their cube roots.
a(n) = n/A000189(n).
Multiplicative with a(p^e) = p^ceiling(e/3).  R. J. Mathar, May 29 2011


MAPLE

f:= n > mul(t[1]^ceil(t[2]/3), t = ifactors(n)[2]):
map(f, [$1..100]); # Robert Israel, Sep 22 2015


MATHEMATICA

cubes=Range[85]^3; Table[Position[Divisible[cubes, i], True, 1, 1][[1, 1]], {i, 85}] (* Harvey P. Dale, Jan 12 2011 *)


PROG

(PARI) a(n)=my(r=1); while(r^3%n!=0, r++); r \\ Anders HellstrÃ¶m, Sep 22 2015
(Sage) [prod([t[0]^(ceil(t[1]/3)) for t in factor(n)]) for n in range(1, 79)] # Danny Rorabaugh, Sep 22 2015


CROSSREFS

Cf. A000188 (inner square root), A019554 (outer square root), A053150 (inner 3rd root), A053164 (inner 4th root), A053166 (outer 4th root), A015052 (outer 5th root), A015053 (outer 6th root).
Cf. A000189, A015050.
Sequence in context: A015052 A053166 A166140 * A243074 A304776 A052410
Adjacent sequences: A019552 A019553 A019554 * A019556 A019557 A019558


KEYWORD

nonn,easy,mult


AUTHOR

R. Muller


EXTENSIONS

Corrected and extended by David W. Wilson


STATUS

approved



