A165430 Table T(n,m) read by rows: the greatest common unitary divisor of n and m, n>=1, 1<=m<=n.

1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 2, 3, 1, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 2, 1, 1, 5, 2, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 3, 4, 1, 3, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 2, 1, 1, 1, 2, 7, 1, 1, 2, 1, 1

Offset: 1

Author

R. J. Mathar, Sep 18 2009

Keywords

• easy
• nonn
• tabl

Comments

The maximum number which appears in row n and also in row m of A077610. The sequence of the counts of 1 in row n=1,2,3,... is 1, 1, 2, 3, 4, 3, 6, 7, 8, 6, 10, 8, 12, 9, 9,...

Examples

			The table starts
1;
1,2
1,1,3
1,1,1,4
1,1,1,1,5
1,2,3,1,1,6
1,1,1,1,1,1,7
1,1,1,1,1,1,1,8
1,1,1,1,1,1,1,1,9
1,2,1,1,5,2,1,1,1,10
		

Links

• Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened
• Pentti Haukkanen, On a gcd-sum function, Aequat. Math. 76 (1-2) (2008) 168-178.
• L. Toth, On the Bi-Unitary Analogues of Euler's Arithmetical Function and the Gcd-Sum Function, JIS 12 (2009) 09.5.2, function (k,n)**.

Crossrefs

Cf. A034444, A275254 (row sums)

Programs

Haskell

import Data.List (intersect)
a165430 n k = last (a077610_row n `intersect` a077610_row k)
a165430_row n = map (a165430 n) [1..n]
a165430_tabl = map a165430_row [1..]
-- Reinhard Zumkeller, Mar 04 2013

Maple

A077610 := proc(n) local a; a := {} ; for d in numtheory[divisors](n) do if gcd(d,n/d) = 1 then a := a union {d} ; fi; od: a; end:
  A165430 := proc(n,m) local cud ; cud := A077610(n) intersect A077610(m) ; max(op(cud)) ; end:
seq(seq(A165430(n,m),m=1..n),n=1..20) ;

Mathematica

A077610[n_] := Module[{a = {}}, Do[If[GCD[d, n/d] == 1, a = a ~Union~ {d}], {d, Divisors[n]}]; a]; A165430[n_, m_] := Module[{cud = A077610[n] ~Intersection~ A077610[m]}, Max[cud]]; Table[Table[A165430[n, m], {m, 1, n}], {n, 1, 20}] // Flatten (* Jean-François Alcover, Dec 12 2013, translated from Maple *)

PARI

udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d);}
T(n,m) = vecmax(setintersect(udivs(n), udivs(m))); \\ Michel Marcus, Oct 11 2015