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%I #19 Jul 28 2016 05:40:44
%S 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,
%T 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,
%U 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
%N Table T(n,m) read by rows: the greatest common unitary divisor of n and m, n>=1, 1<=m<=n.
%C 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,...
%H Reinhard Zumkeller, <a href="/A165430/b165430.txt">Rows n = 1..120 of triangle, flattened</a>
%H Pentti Haukkanen, <a href="http://dx.doi.org/10.1007/s00010-007-2923-5">On a gcd-sum function</a>, Aequat. Math. 76 (1-2) (2008) 168-178.
%H L. Toth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Toth2/toth5.html">On the Bi-Unitary Analogues of Euler's Arithmetical Function and the Gcd-Sum Function</a>, JIS 12 (2009) 09.5.2, function (k,n)**.
%e The table starts
%e 1;
%e 1,2
%e 1,1,3
%e 1,1,1,4
%e 1,1,1,1,5
%e 1,2,3,1,1,6
%e 1,1,1,1,1,1,7
%e 1,1,1,1,1,1,1,8
%e 1,1,1,1,1,1,1,1,9
%e 1,2,1,1,5,2,1,1,1,10
%p 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:
%p A165430 := proc(n,m) local cud ; cud := A077610(n) intersect A077610(m) ; max(op(cud)) ; end:
%p seq(seq(A165430(n,m),m=1..n),n=1..20) ;
%t 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 *)
%o (Haskell)
%o import Data.List (intersect)
%o a165430 n k = last (a077610_row n `intersect` a077610_row k)
%o a165430_row n = map (a165430 n) [1..n]
%o a165430_tabl = map a165430_row [1..]
%o -- _Reinhard Zumkeller_, Mar 04 2013
%o (PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d);}
%o T(n,m) = vecmax(setintersect(udivs(n), udivs(m))); \\ _Michel Marcus_, Oct 11 2015
%Y Cf. A034444, A275254 (row sums)
%K easy,nonn,tabl
%O 1,3
%A _R. J. Mathar_, Sep 18 2009
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