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 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 (list; graph; refs; listen; history; text; internal format)
 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^t-1)} 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

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Last modified April 13 09:12 EDT 2021. Contains 342935 sequences. (Running on oeis4.)