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A384046 Triangle in which the n-th row gives the numbers from 1 to n whose largest divisor that is a unitary divisor of n is 1.

%I A384046 #12 May 24 2025 03:32:22
%S A384046 1,1,1,2,1,2,3,1,2,3,4,1,5,1,2,3,4,5,6,1,2,3,4,5,6,7,1,2,3,4,5,6,7,8,
%T A384046 1,3,7,9,1,2,3,4,5,6,7,8,9,10,1,2,5,7,10,11,1,2,3,4,5,6,7,8,9,10,11,
%U A384046 12,1,3,5,9,11,13,1,2,4,7,8,11,13,14,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
%N A384046 Triangle in which the n-th row gives the numbers from 1 to n whose largest divisor that is a unitary divisor of n is 1.
%H A384046 Amiram Eldar, <a href="/A384046/b384046.txt">Table of n, a(n) for n = 1..10204</a> (first 170 rows flattened)
%H A384046 Eckford Cohen, <a href="https://doi.org/10.1007/BF01180473">Arithmetical functions associated with the unitary divisors of an integer</a>, Mathematische Zeitschrift, Vol. 74 (1960), pp. 66-80.
%F A384046 T(n, 1) = 1.
%e A384046 Triangle begins:
%e A384046   1,
%e A384046   1,
%e A384046   1, 2,
%e A384046   1, 2, 3,
%e A384046   1, 2, 3, 4,
%e A384046   1, 5,
%e A384046   1, 2, 3, 4, 5, 6,
%e A384046   1, 2, 3, 4, 5, 6, 7,
%e A384046   1, 2, 3, 4, 5, 6, 7, 8,
%e A384046   1, 3, 7, 9
%t A384046 udiv[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &]; uGCD[n_, k_] := Max[Intersection[udiv[n], Divisors[k]]]; row[n_] := Select[Range[n], uGCD[n, #] == 1 &]; Array[row, 10] // Flatten
%o A384046 (PARI) udiv(n) = select(x -> gcd(x, n/x) == 1, divisors(n));
%o A384046 ugcd(n, k) = vecmax(setintersect(udiv(n), divisors(k)));
%o A384046 row(n) = select(x -> ugcd(n, x) == 1, vector(n, i, i));
%Y A384046 The unitary analog of A038566.
%Y A384046 Cf. A047994 (row lengths), A333576 (row sums), A077610, A225174, A384047.
%K A384046 nonn,tabf,easy
%O A384046 1,4
%A A384046 _Amiram Eldar_, May 18 2025