

A229964


Number of pairs of integers q1, q2 with 1 < q1 < q2 < n such that if we randomly pick an integer in {1, ..., n}, the event of being divisible by q1 is independent of being divisible by q2.


6



0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 3, 0, 3, 2, 1, 0, 4, 0, 5, 1, 3, 0, 8, 0, 4, 3, 4, 0, 10, 0, 7, 3, 5, 2, 9, 0, 6, 4, 9, 0, 13, 0, 12, 6, 6, 0, 16, 0, 9, 6, 9, 0, 14, 1, 12, 3, 8, 0, 25, 0, 12, 10, 11, 4, 17, 0, 12, 7, 17, 0, 25, 0, 14, 12, 14, 2, 21, 0, 21, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)



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


CROSSREFS

The n such that a(n) = m for various m are given by: m=0, A166684; m=1, A229965; m=2, A082663; m=3, A229966; m=4, A229967.
Sequence in context: A105824 A171911 A180193 * A309722 A070298 A024938
Adjacent sequences: A229961 A229962 A229963 * A229965 A229966 A229967


KEYWORD

nonn


AUTHOR

Eric M. Schmidt, Oct 04 2013


STATUS

approved



