OFFSET
1,19
REFERENCES
O. Hölder. Die Gruppen mit quadratfreier Ordnungszahl. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse, pages 211-219 (1895).
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
I. Ganev, Groups of a Square-Free order, Rose-Hulman Undergraduate Mathematics Journal: Vol. 11 : Iss. 1 , Article 7 (2010).
PROG
(Python)
from math import isqrt, prod
from itertools import combinations
from sympy import mobius, primefactors, npartitions, factorint
def A375483(n):
def f(x): return n+x-sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
a = set(primefactors(m))
return sum(prod((p**sum(1 for q in b if q%p==1)-1)//(p-1) for p in a-set(b)) for l in range(0, len(a)+1) for b in combinations(a, l))-prod(map(npartitions, factorint(m).values()))
CROSSREFS
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Aug 17 2024
STATUS
approved