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 A000190 Number of solutions to x^4 == 0 (mod n). 15
 1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 8, 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, 8, 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, 8, 27, 1, 1, 2, 1, 1, 1, 4, 1, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Shadow transform of fourth powers A000583. - 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. Lorenz Halbeisen, A number-theoretic conjecture and its implication for set theory, Acta Math. Univ. Comenianae 74(2) (2005), 243-254. Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5 (1999), 138-150. OEIS Wiki, Shadow transform. N. J. A. Sloane, Transforms. FORMULA Multiplicative with a(p^e) = p^[3e/4]. - David W. Wilson, Aug 01 2001 MATHEMATICA Array[ Function[ n, Count[ Array[ PowerMod[ #, 4, n ]&, n, 0 ], 0 ] ], 100 ] f[p_, e_] := p^Floor[3*e/4]; 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]^(3*f[i, 2]\4)) \\ Charles R Greathouse IV, Jun 07 2013 CROSSREFS Sequence in context: A104445 A359762 A000189 * A348037 A003557 A073752 Adjacent sequences: A000187 A000188 A000189 * A000191 A000192 A000193 KEYWORD nonn,mult,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified November 30 18:31 EST 2023. Contains 367461 sequences. (Running on oeis4.)