

A119348


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


8



1, 1, 2, 3, 1, 3, 4, 1, 2, 3, 4, 5, 6, 7, 1, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 3, 4, 9, 10, 12, 13, 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 1, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
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OFFSET

1,3


COMMENTS

Row n contains A119347(n) terms. In row n the first term is 1 and the last term is sigma(n) (=sum of the divisors of n =A000203(n)). If row n contains all numbers from 1 to sigma(n), then n is called a practical number (A005153).


LINKS

T. D. Noe, Rows n=1..100, flattened


EXAMPLE

Row 5 is 1,5,6, the possible sums obtained from the divisors 1 and 5 of 5.
Triangle starts:
1;
1,2,3;
1,3,4;
1,2,3,4,5,6,7;
1,5,6;
1,2,3,4,5,6,7,8,9,10,11,12;
1,7,8;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15;
1,3,4,9,10,12,13;


MAPLE

with(numtheory): with(linalg): sums:=proc(n) local dl, t: dl:=convert(divisors(n), list): t:=tau(n): {seq(innerprod(dl, convert(2^t+i, base, 2)[1..t]), i=1..2^t1)} end: for n from 1 to 12 do sums(n) od; # yields sequence in triangular form


CROSSREFS

Cf. A000203, A005153, A119347.
Sequence in context: A238793 A240677 A030306 * A282935 A181974 A322589
Adjacent sequences: A119345 A119346 A119347 * A119349 A119350 A119351


KEYWORD

nonn,tabf


AUTHOR

Emeric Deutsch, May 15 2006


STATUS

approved



