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 A000189 Number of solutions to x^3 == 0 (mod n). 15
 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 Henry Bottomley, Some Smarandache-type multiplicative sequences. Steven 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 ] f[p_, e_] := p^Floor[2*e/3]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2020 *) 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 STATUS approved

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)