OFFSET
1,2
COMMENTS
Shadow transform of A034262. - Michel Marcus, Jun 06 2013
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..10000
Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150; see Definition 7 for the shadow transform.
N. J. A. Sloane, Transforms.
FORMULA
Multiplicative with a(2^1) = 2, a(2^e) = 1 for e > 1, a(p^e) = 3 for p mod 4 == 1, a(p^e) = 1 for p mod 4 == 3. - Andrew Howroyd, Jul 15 2018
MATHEMATICA
a[n_] := If[n == 1, 1, Product[{p, e} = pe; If[p == 2, If[e == 1, 2, 1], If[Mod[p, 4] == 1, 3, 1]], {pe, FactorInteger[n]}]];
a /@ Range[1, 100] (* Jean-François Alcover, Sep 20 2019 *)
PROG
(PARI) a(n)={my(v=vector(n)); sum(i=0, n-1, lift(Mod(i, n)^3 + i) == 0)} \\ Andrew Howroyd, Jul 15 2018
(PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, if(e==1, 2, 1), if(p%4==1, 3, 1)))} \\ Andrew Howroyd, Jul 15 2018
CROSSREFS
KEYWORD
mult,nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 06 2003
EXTENSIONS
More terms from David Wasserman, Jun 17 2005
STATUS
approved