OFFSET
1,10
COMMENTS
a(n,1) = 0, for all n. a(1,m) = d(m)-1, for all m.
From Luc Rousseau, Jul 27 2018: (Start)
a(.,m) is periodic with period m.
a(n,m) is the number of nonzero elements S(n) and S(n+m) have in common, where S(n) denotes the set of complex numbers k*(1-exp(i*2*Pi*n/k), for k positive integer. See illustration, section links.
(End)
LINKS
FORMULA
a(n,m) = d(m) - d(gcd(n,m)), where d(m) = A000005(m).
EXAMPLE
From Andrew Howroyd, Jul 27 2018: (Start)
Array begins
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ...
1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 ...
2 1 2 0 2 1 2 0 2 1 2 0 2 1 2 0 2 1 ...
1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 ...
3 2 2 2 3 0 3 2 2 2 3 0 3 2 2 2 3 0 ...
1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 ...
3 2 3 1 3 2 3 0 3 2 3 1 3 2 3 0 3 2 ...
2 2 1 2 2 1 2 2 0 2 2 1 2 2 1 2 2 0 ...
...
(End)
MAPLE
A159459 := proc(n, m) numtheory[tau](m)-numtheory[tau](gcd(n, m)) ; end: for d from 2 to 20 do for m from 1 to d-1 do n := d-m ; printf("%d, ", A159459(n, m)) ; od: od: # R. J. Mathar, Apr 16 2009
MATHEMATICA
Table[DivisorSigma[0, #] - DivisorSigma[0, GCD[n, #]] &[m - n + 1], {m, 13}, {n, m, 1, -1}] // Flatten (* Michael De Vlieger, Jul 30 2018 *)
PROG
(PARI) \\ port of R.J. Mathar's Maple program
a(n, m)=numdiv(m)-numdiv(gcd(n, m))
for(d=2, 20, for(m=1, d-1, n=d-m; print1(a(n, m), ", "))) \\ Luc Rousseau, Jul 27 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Leroy Quet, Apr 12 2009
EXTENSIONS
2 terms corrected by R. J. Mathar, Apr 16 2009
STATUS
approved