OFFSET
1,3
LINKS
Michel Marcus, Table of n, a(n) for n = 1..10000
R. L. Graham, J. C. Lagarias, C. L. Mallows, Allan Wilks and C. H. Yan, Apollonian Circle Packings: Number Theory, arXiv:math/0009113 [math.NT], 2000-2003.
R. L. Graham, J. C. Lagarias, C. L. Mallows, Allan Wilks and C. H. Yan, Apollonian Circle Packings: Number Theory, J. Number Theory, 100 (2003), 1-45.
FORMULA
See Theorem 4.3 in Graham et al. link.
MATHEMATICA
chim4[p_] := If[p != 2, (-1)^((p - 1)/2), 0];
delta[n_] := If[Mod[n, 4] == 2, 1, 0];
a[n_] := If[n == 1, 1, n/4 Product[1 - chim4[p]/p, {p, FactorInteger[n][[All, 1]]}] + 2^(PrimeNu[n] - delta[n] - 1)];
Array[a, 72] (* Jean-François Alcover, Jan 26 2019, from PARI *)
PROG
(PARI) chim4(p) = if (p % 2, (-1)^((p-1)/2), 0);
delta(n) = if ((n % 4)==2, 1, 0);
a(n) = {if (n==1, 1, f = factor(n)[, 1]; n/4*prod(k=1, #f~, (1 - chim4(f[k])/f[k])) + 2^(omega(n)-delta(n)-1)); } \\ Michel Marcus, May 13 2015
CROSSREFS
KEYWORD
AUTHOR
Jeffrey C. Lagarias (lagarias(AT)umich.edu)
EXTENSIONS
Thanks to Robert G. Wilson v for pointing out that one of the terms was wrong.
Offset changed to 1 and more terms from Michel Marcus, May 13 2015
STATUS
approved