# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a208460 Showing 1-1 of 1 %I A208460 #39 Feb 21 2017 08:16:26 %S A208460 1,2,3,2,4,5,4,3,6,7,6,4,8,6,9,8,5,10,11,10,9,8,6,12,13,12,7,14,12,10, %T A208460 15,14,12,8,16,17,16,15,12,9,18,19,18,16,15,10,20,18,14,21,20,11,22, %U A208460 23,22,21,20,18,16,12,24,20,25,24,13,26,24,18,27,26,24 %N A208460 Triangle read by rows: T(n,k) = n minus the k-th proper divisor of n. %C A208460 Conjecture: one of the divisors of T(n,k) is also the k-th divisor of n. In a diagram of the structure of divisors of the natural numbers (see link) the mentioned divisors of the elements of row n are located on a straight line to 45 degrees from the vertical straight line that contains the divisors of n, therefore the divisors of n are predictable. %H A208460 Alois P. Heinz, Rows n = 2..1540, flattened %H A208460 Omar E. Pol, Illustration of the structure of divisors of the natural numbers, for n = 1..16 %F A208460 T(n,k) = n - A027751(n,k). %e A208460 Written as a triangle starting from n = 2: %e A208460 1; %e A208460 2; %e A208460 3, 2; %e A208460 4; %e A208460 5, 4, 3; %e A208460 6; %e A208460 7, 6, 4; %e A208460 8, 6; %e A208460 9, 8, 5; %e A208460 10; %e A208460 11, 10, 9, 8, 6; %e A208460 12; %p A208460 with (numtheory): %p A208460 T:= n-> map(x-> n-x, sort([(divisors(n) minus {n})[]]))[]: %p A208460 seq (T(n), n=2..50); # _Alois P. Heinz_, Apr 11 2012 %t A208460 T[n_] := Most[n-Divisors[n]]; Table[T[n], {n, 2, 50}] // Flatten (* _Jean-François Alcover_, Feb 21 2017 *) %Y A208460 Column 1 is A000027. Row n has length A032741(n). Row sums give the positives A094471. Right border is A060681. %Y A208460 Cf. A000005, A027750, A027751. %K A208460 nonn,tabf %O A208460 2,2 %A A208460 _Omar E. Pol_, Feb 28 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE