cp's OEIS Frontend

A384047 Triangle read by rows: T(n, k) for 1 <= k <= n is the largest divisor of k that is a unitary divisor of n.

%I A384047 #11 May 24 2025 03:32:26
%S A384047 1,1,2,1,1,3,1,1,1,4,1,1,1,1,5,1,2,3,2,1,6,1,1,1,1,1,1,7,1,1,1,1,1,1,
%T A384047 1,8,1,1,1,1,1,1,1,1,9,1,2,1,2,5,2,1,2,1,10,1,1,1,1,1,1,1,1,1,1,11,1,
%U A384047 1,3,4,1,3,1,4,3,1,1,12,1,1,1,1,1,1,1,1,1,1,1,1,13
%N A384047 Triangle read by rows: T(n, k) for 1 <= k <= n is the largest divisor of k that is a unitary divisor of n.
%H A384047 Amiram Eldar, <a href="/A384047/b384047.txt">Table of n, a(n) for n = 1..10585</a> (first 145 rows flattened)
%F A384047 T(n, 1) = 1.
%F A384047 T(n, n) = n.
%F A384047 T(n, k) <= A050873(n, k) = gcd(n, k), with equality if n is squarefree (A005117).
%e A384047 Triangle begins:
%e A384047   1
%e A384047   1, 2
%e A384047   1, 1, 3
%e A384047   1, 1, 1, 4
%e A384047   1, 1, 1, 1, 5
%e A384047   1, 2, 3, 2, 1, 6
%e A384047   1, 1, 1, 1, 1, 1, 7
%e A384047   1, 1, 1, 1, 1, 1, 1, 8
%e A384047   1, 1, 1, 1, 1, 1, 1, 1, 9
%e A384047   1, 2, 1, 2, 5, 2, 1, 2, 1, 10
%t A384047 udiv[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &]; T[n_, k_] := Max[Intersection[udiv[n], Divisors[k]]]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten
%o A384047 (PARI) udiv(n) = select(x -> gcd(x, n/x) == 1, divisors(n));
%o A384047 T(n, k) = vecmax(setintersect(udiv(n), divisors(k)));
%Y A384047 Cf. A005117, A050873, A077610, A145388 (row sums), A165430, A225174, A384046.
%Y A384047 Upper right triangle of A322482.
%K A384047 nonn,tabl,easy
%O A384047 1,3
%A A384047 _Amiram Eldar_, May 18 2025