A193280 - OEIS

%I #13 Mar 02 2019 23:34:05

%S 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 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 2,3,4,5,6,7,8,9,10,11,12,13,14,15

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

%C 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 Nathaniel Johnston, <a href="/A193280/b193280.txt">Rows 1..150, flattened</a>

%e 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 Triangle starts:

%e   0;

%e   1;

%e   1;

%e   1,2,3;

%e   1;

%e   1,2,3,4,5,6;

%e   1;

%e   1,2,3,4,5,6,7;

%e   1,3,4;

%e   1,2,3,5,6,7,8;

%e   1;

%e   1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16;

%p 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 Cf. A119347, A119348, A193279.

%K nonn,tabf

%O 1,5

%A _Michael Engling_, Jul 20 2011