OFFSET
1,14
COMMENTS
The p-rank of a finite abelian group G is equal to log_p(#{x belongs to G : x^p = 1}) where p is a prime number. In this case, G is the class group of Q(sqrt(-k)), and #{x belongs to G : x^p = 1} is the number of genera of Q(sqrt(-k)) (cf. A003643).
LINKS
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
FORMULA
MATHEMATICA
PrimeNu[#*If[Mod[-#, 4]>1, 4, 1]] - 1& /@ Select[Range[200], SquareFreeQ] (* Jean-François Alcover, Aug 02 2019 *)
PROG
(PARI) for(n=1, 200, if(issquarefree(n), print1(omega(n*if((-n)%4>1, 4, 1)) - 1, ", ")))
(Sage)
def A319662_list(len):
L = []
for n in (1..len):
if is_squarefree(n):
if (-n) % 4 > 1: n <<= 2
L.append(sloane.A001221(n) - 1)
return L
print(A319662_list(141)) # Peter Luschny, Oct 15 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Sep 25 2018
STATUS
approved