OFFSET
1,12
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Rosemary Sullivan and Neil Watling, Independent Divisibility Pairs on the Set of Integers from 1 to N, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 13, Paper A65, 2013.
EXAMPLE
If n = 12, then q1 = 2 and q2 = 5 satisfy the condition as the probability of an integer in {1, ..., 12} being divisible by 2 is 1/2, by 5 is 1/6, and by both 2 and 5 is 1/12.
PROG
(Sage)
def A229964(n) : return sum(sum(dprob(q1, n) * dprob(q2, n) == dprob(lcm(q1, q2), n) for q2 in range(q1+1, n)) for q1 in n.divisors() if q1 not in [1, n])
def dprob(q, n) : return (n // q)/n
(Python)
from math import lcm
from sympy import divisors
def A229964(n): return sum(1 for d in divisors(n, generator=True) for e in range(d+1, n) if 1<d<n and (n//d)*(n//e)==n*(n//lcm(d, e))) # Chai Wah Wu, Aug 09 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Oct 04 2013
STATUS
approved