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A384244 Triangle in which the n-th row gives the numbers k from 1 to n such that the greatest common unitary divisor of k and n is 1.

%I A384244 #9 May 27 2025 01:17:52
%S A384244 1,1,1,2,1,2,3,1,2,3,4,1,4,5,1,2,3,4,5,6,1,2,3,4,5,6,7,1,2,3,4,5,6,7,
%T A384244 8,1,3,4,7,8,9,1,2,3,4,5,6,7,8,9,10,1,2,5,7,8,9,10,11,1,2,3,4,5,6,7,8,
%U A384244 9,10,11,12,1,3,4,5,8,9,11,12,13,1,2,4,7,8,9,11,13,14
%N A384244 Triangle in which the n-th row gives the numbers k from 1 to n such that the greatest common unitary divisor of k and n is 1.
%H A384244 Amiram Eldar, <a href="/A384244/b384244.txt">Table of n, a(n) for n = 1..10349</a> (first 160 rows flattened)
%H A384244 László Tóth, <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>, Journal of Integer Sequences, Vol. 12 (2009), Article 09.5.2.
%e A384244 Triangle begins:
%e A384244   1
%e A384244   1
%e A384244   1, 2
%e A384244   1, 2, 3
%e A384244   1, 2, 3, 4
%e A384244   1, 4, 5
%e A384244   1, 2, 3, 4, 5, 6
%e A384244   1, 2, 3, 4, 5, 6, 7
%e A384244   1, 2, 3, 4, 5, 6, 7, 8
%e A384244   1, 3, 4, 7, 8, 9
%t A384244 udiv[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &];
%t A384244 ugcd[n_, m_] := Max[Intersection[udiv[n], udiv[m]]];
%t A384244 row[n_] := Select[Range[n], ugcd[n, #] == 1 &]; Array[row, 15] // Flatten
%o A384244 (PARI) udiv(n) = select(x -> gcd(x, n/x) == 1, divisors(n));
%o A384244 ugcd(n, m) = vecmax(setintersect(udiv(n), udiv(m)));
%o A384244 row(n) = select(x -> ugcd(n, x) == 1, vector(n, i, i));
%Y A384244 The bi-unitary analog of A038566.	
%Y A384244 Cf. A116550 (row lengths), A200723 (row sums), A077610, A089912, A165430, A225174, A064379 (infinitary analog), A384046 (unitary analog).
%K A384244 nonn,tabf,easy
%O A384244 1,4
%A A384244 _Amiram Eldar_, May 23 2025