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A225174
Square array read by antidiagonals: T(m,n) = greatest common unitary divisor of m and n.
4
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
1,5
REFERENCES
M. Lal, H. Wareham and R. Mifflin, Iterates of the bi-unitary totient function, Utilitas Math., 10 (1976), 347-350.
FORMULA
T(m,n) = T(n,m) = A165430(n,m).
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
See A034444, A077610 for unitary divisors of n.
Different from A059895.
Sequence in context: A306345 A204125 A204127 * A059895 A368328 A321167
KEYWORD
nonn,tabl,look
AUTHOR
N. J. A. Sloane, May 01 2013
STATUS
approved