LINKS
Chai Wah Wu, <a href="/A003049/b003049_3.txt">Table of n, a(n) for n = 1..88</a> (terms 1..60 from Max Alekseyev)
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Revision History for A003049
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
LINKS
Max Alekseyev, Chai Wah Wu, <a href="/A003049/b003049_3.txt">Table of n, a(n) for n = 1..88</a> (terms 1..60</a> from Max Alekseyev)
STATUS
approved
editing
STATUS
reviewed
approved
STATUS
proposed
reviewed
STATUS
editing
proposed
PROG
return sum(mobius(n//d)*c(d) for d in divisors(n, generator=True))//n # Chai Wah Wu, Jul 03 2024
PROG
(Python)
from functools import lru_cache
from itertools import combinations
from fractions import Fraction
from math import prod, gcd, factorial
from sympy import mobius, divisors
from sympy.utilities.iterables import partitions
def A003049(n):
@lru_cache(maxsize=None)
def b(n): return int(sum(Fraction(1<<sum(p[r]*p[s]*gcd(r, s) for r, s in combinations(p.keys(), 2))+sum(((q>>1)-1)*r+(q*r*(r-1)>>1) for q, r in p.items())+any(q&1 for q in p), prod(q**r*factorial(r) for q, r in p.items())) for p in partitions(n)))
@lru_cache(maxsize=None)
def c(n): return n*b(n)-sum(c(k)*b(n-k) for k in range(1, n))
return sum(mobius(n//d)*c(d) for d in divisors(n, generator=True))//n # Chai Wah Wu, Jul 03 2024
STATUS
approved
editing