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

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

Cf. A119347, A119348, A193279.

Sequence in context: A351651 A157813 A111879 * A114732 A123338 A152735

Adjacent sequences: A193277 A193278 A193279 * A193281 A193282 A193283

Keyword

nonn,tabf

Author

Michael Engling, Jul 20 2011

Status

approved