OFFSET
1,2
COMMENTS
A kind of 2-dimensional version of the Euler phi function A000010.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
FORMULA
a(m, n) = Sum_{g=1..min(m,n)} floor(m/g) * floor(n/g) * moebius(g). - Andrew Howroyd, Sep 17 2017
a(m, n) <= m*n - Sum_{i=1..m} ( (i - phi(i)) * floor(n / i) ).
Conjecture: a(m, n) ~ mn - sum_1^m{ (i - phi(i)) (n / i) } = n sum_1^m{ phi(i) / i } ~ 6mn / pi^2 as m -> oo.
a(m, n) = A049687(m, n) + 2. - Andrew Howroyd, Sep 17 2017
EXAMPLE
a(2, 5) = 8 since of the 10 possible pairs all but (2, 2) and (2, 4) are coprime.
The terms given correspond to the following values:
1 = a(1, 1)
2 2 = a(2, 1), a(1, 2)
3 3 3 = a(3, 1), a(2, 2), a(1, 3), etc.
4 5 5 4
5 6 7 6 5
6 8 9 9 8 6
7 9 12 11 12 9 7
8 11 13 15 15 13 11 8
9 12 16 16 19 16 16 12 9
10 14 18 20 21 21 20 18 14 10
etc.
PROG
(PARI) a(m, n) = sum(g=1, min(m, n), (m\g)*(n\g)*moebius(g)); \\ Andrew Howroyd, Sep 17 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Hugo van der Sanden, Nov 22 2008
STATUS
approved