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A193280 Triangle read by rows: row n contains, in increasing order, all the distinct sums of distinct proper divisors of n.

%I A193280 #13 Mar 02 2019 23:34:05
%S A193280 0,1,1,1,2,3,1,1,2,3,4,5,6,1,1,2,3,4,5,6,7,1,3,4,1,2,3,5,6,7,8,1,1,2,
%T A193280 3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,1,2,3,7,8,9,10,1,3,4,5,6,8,9,1,
%U A193280 2,3,4,5,6,7,8,9,10,11,12,13,14,15
%N A193280 Triangle read by rows: row n contains, in increasing order, all the distinct sums of distinct proper divisors of n.
%C A193280 Row n > 1 contains A193279(n) terms. In row n the first term is 1 and the last term is sigma(n) - n (= A000203(n) - n). Row 1 contains 0 because 1 has no proper divisors.
%H A193280 Nathaniel Johnston, <a href="/A193280/b193280.txt">Rows 1..150, flattened</a>
%e A193280 Row 10 is 1,2,3,5,6,7,8 the possible sums obtained from the proper divisors 1, 2, and 5 of 10.
%e A193280 Triangle starts:
%e A193280   0;
%e A193280   1;
%e A193280   1;
%e A193280   1,2,3;
%e A193280   1;
%e A193280   1,2,3,4,5,6;
%e A193280   1;
%e A193280   1,2,3,4,5,6,7;
%e A193280   1,3,4;
%e A193280   1,2,3,5,6,7,8;
%e A193280   1;
%e A193280   1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16;
%p A193280 with(linalg): print(0); for n from 2 to 12 do dl:=convert(numtheory[divisors](n) minus {n}, list): t:=nops(dl): print(op({seq(innerprod(dl, convert(2^t+i, base, 2)[1..t]), i=1..2^t-1)})): od: # _Nathaniel Johnston_, Jul 23 2011
%Y A193280 Cf. A119347, A119348, A193279.
%K A193280 nonn,tabf
%O A193280 1,5
%A A193280 _Michael Engling_, Jul 20 2011