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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.
2
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, 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, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
OFFSET
1,5
COMMENTS
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.
LINKS
Nathaniel Johnston, Rows 1..150, flattened
EXAMPLE
Row 10 is 1,2,3,5,6,7,8 the possible sums obtained from the proper divisors 1, 2, and 5 of 10.
Triangle starts:
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;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16;
MAPLE
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
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Michael Engling, Jul 20 2011
STATUS
approved