A225174 Square array read by antidiagonals: T(m,n) = greatest common unitary divisor of m and n.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 5, 1, 1, 1, 1, 5, 1, 3, 1, 1

Offset: 1

Author

N. J. A. Sloane, May 01 2013

Keywords

• nonn
• tabl
• look

Examples

			Array begins
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, ...
1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, ...
1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, ...
1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, ...
1, 2, 3, 1, 1, 6, 1, 1, 1, 2, 1, 3, ...
1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, ...
...
The unitary divisors of 3 are 1 and 3, those of 6 are 1,2,3,6; so T(6,3) = T(3,6) = 3.
		

References

• M. Lal, H. Wareham and R. Mifflin, Iterates of the bi-unitary totient function, Utilitas Math., 10 (1976), 347-350.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20100; the first 200 antidiagonals of the array

Crossrefs

See A034444, A077610 for unitary divisors of n.

Different from A059895.

Programs

Maple

# returns the greatest common unitary divisor of m and n
f:=proc(m,n)
local i,ans;
ans:=1;
for i from 1 to min(m,n) do
if ((m mod i) = 0) and (igcd(i,m/i) = 1)  then
   if ((n mod i) = 0) and (igcd(i,n/i) = 1)  then ans:=i; fi;
fi;
od;
ans; end;

Mathematica

f[m_, n_] := Module[{i, ans=1}, For[i=1, i<=Min[m, n], i++, If[Mod[m, i]==0 && GCD[i, m/i]==1, If[Mod[n, i]==0 && GCD[i, n/i]==1, ans=i]]]; ans];
Table[f[m-n+1, n], {m, 1, 14}, {n, 1, m}] // Flatten (* Jean-François Alcover, Jun 19 2018, translated from Maple *)

PARI

up_to = 20100; \\ = binomial(200+1,2)
A225174sq(m,n) = { my(a=min(m,n),b=max(m,n),md=0); fordiv(a,d,if(0==(b%d)&&1==gcd(d,a/d)&&1==gcd(d,b/d),md=d)); (md); };
A225174list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, if(i++ > up_to, return(v)); v[i] = A225174sq((a-(col-1)),col))); (v); };
v225174 = A225174list(up_to);
A225174(n) = v225174[n]; \\ Antti Karttunen, Nov 28 2018

Formula

T(m,n) = T(n,m) = A165430(n,m).