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A000189 Number of solutions to x^3 == 0 (mod n). 14
1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 9, 2, 1, 1, 1, 8, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 4, 7, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 2, 1, 1, 3, 16, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 5, 2, 1, 1, 1, 4, 9, 1, 1, 2, 1, 1, 1, 4, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Shadow transform of the cubes A000578. - Michel Marcus, Jun 06 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

H. Bottomley, Some Smarandache-type multiplicative sequences.

S. R. Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math/0604465 [math.NT], 2006-2016.

Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. (ps, pdf); see Definition 7 for the shadow transform.

OEIS Wiki, Shadow transform.

N. J. A. Sloane, Transforms.

FORMULA

Multiplicative with a(p^e) = p^[2e/3]. - David W. Wilson, Aug 01 2001

a(n) = n/A019555(n). - Petros Hadjicostas, Sep 15 2019

EXAMPLE

a(4) = 2 because 0^3 == 0, 1^3 == 1, 2^3 == 0, and 3^3 == 3 (mod 4); also, a(9) = 3 because 0^3 = 0, 3^3 == 0, and 6^3 = 0 (mod 9), while x^3 =/= 0 (mod 9) for x = 1, 2, 4, 5, 7, 8. - Petros Hadjicostas, Sep 16 2019

MATHEMATICA

Array[ Function[ n, Count[ Array[ PowerMod[ #, 3, n ]&, n, 0 ], 0 ] ], 100 ]

PROG

(PARI) a(n)=my(f=factor(n)); prod(i=1, #f[, 1], f[i, 1]^(2*f[i, 2]\3)) \\ Charles R Greathouse IV, Jun 06 2013

CROSSREFS

Cf. A000578, A019555.

Sequence in context: A220632 A125653 A104445 * A000190 A003557 A073752

Adjacent sequences:  A000186 A000187 A000188 * A000190 A000191 A000192

KEYWORD

nonn,mult,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)