A000190 Number of solutions to x^4 == 0 (mod n).
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
Offset: 1
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.
Crossrefs
Cf. A000583.
Programs
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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 *)
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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
Formula
Multiplicative with a(p^e) = p^[3e/4]. - David W. Wilson, Aug 01 2001
Dirichlet g.f.: zeta(4*s-3) * Product_{p prime} (1 + 1/p^s + 1/p^(2*s-1) + 1/p^(3*s-2)). - Amiram Eldar, Dec 18 2023
Comments