cp's OEIS Frontend

A233773 Triangle read by rows in which row n lists the proper divisors of n together with -n.

%I A233773 #11 Feb 16 2025 08:33:21
%S A233773 -1,1,-2,1,-3,1,2,-4,1,-5,1,2,3,-6,1,-7,1,2,4,-8,1,3,-9,1,2,5,-10,1,
%T A233773 -11,1,2,3,4,6,-12,1,-13,1,2,7,-14,1,3,5,-15,1,2,4,8,-16,1,-17,1,2,3,
%U A233773 6,9,-18,1,-19,1,2,4,5,10,-20,1,3,7,-21,1,2,11,-22,1,-23
%N A233773 Triangle read by rows in which row n lists the proper divisors of n together with -n.
%C A233773 The same as A027750 but with the last term of every row multiplied by -1.
%C A233773 The sum of row n gives the abundance of n.
%H A233773 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Abundance.html">Abundance</a>
%H A233773 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuasiperfectNumber.html">Quasiperfect Number</a>
%e A233773 Written as an irregular triangle in which row n has length A000005(n) the sequence begins:
%e A233773 -1;
%e A233773 1, -2;
%e A233773 1, -3;
%e A233773 1, 2, -4;
%e A233773 1, -5;
%e A233773 1, 2, 3, -6;
%e A233773 1, -7;
%e A233773 1, 2, 4, -8;
%e A233773 1, 3, -9;
%e A233773 1, 2, 5, -10;
%e A233773 1, -11;
%e A233773 1, 2, 3, 4, 6, -12;
%e A233773 ...
%t A233773 Flatten[Table[Join[{Most[Divisors[n]]},{-n}],{n,30}]] (* _Harvey P. Dale_, Feb 20 2016 *)
%Y A233773 Row sums give A033880.
%Y A233773 Cf. A000005, A000203, A000396, A001065, A005100, A005101, A027750, A027751, A033879.
%Y A233773 Cf. A137510, A163870.
%K A233773 sign,tabf
%O A233773 1,3
%A A233773 _Omar E. Pol_, Dec 31 2013