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 A120577 Irregular array where the n-th row are the divisors, not occurring earlier in the sequence, of the sum of the terms in all previous rows. a(1)=3. 4
 3, 1, 2, 4, 5, 10, 25, 50, 20, 100, 11, 22, 44, 55, 110, 220, 31, 62, 341, 682, 29, 58, 899, 1798, 79, 158, 2291, 4582, 37, 74, 148, 316, 2923, 5846, 11692, 8, 4091, 8182, 16364, 32728, 7, 21, 4481, 13443, 31367, 94101, 23, 449, 529, 10327, 237521, 17, 34, 85, 170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Is this sequence a permutation of the positive integers? LINKS Michael De Vlieger, Table of n, a(n) for n = 1..12111 (rows 1 <= n <= 177) EXAMPLE Array begins:    3    1    2,  4    5, 10   25   50 Now these terms add up to 100. So row 7 is the divisors of 100 which do not occur earlier in the sequence. 1,2,4,5,10,25 and 50 occur in earlier rows, so row 7 is (20,100). From Michael De Vlieger, Oct 03 2017: (Start) Lengths of rows of a(n) and relation to number of divisors of the sum of terms in all previous rows. Key: n = index; m = length of row n; k = sum of the terms in all previous rows. tau(k(n-1)) = number of divisors of k of the previous row. delta = tau(k(n-1)) - m: i.e., divisors of k(n - 1) not in row n of this sequence. .    n  tau(k(n-1))    m    delta           k    ----------------------------------------    1        -        3      -             3    2        2        1      1             4    3        3        2      1            10    4        4        2      2            25    5        3        1      2            50    6        6        1      5           100    7        9        2      7           220    8       12        6      6           682    9        8        4      4          1798   10        8        4      4          4582   11        8        4      4         11692   12       12        7      5         32728   13        8        5      3         94101   14        8        6      2        237521   15        6        5      1        486370   16       16       12      4       1413640   17       32       25      7       4653590   18       16       11      5      13394637   19       12       10      2      33108197   20        8        6      2      69019691   ...   (End) MATHEMATICA f[t_] := Flatten[Append[t, Select[Divisors[Plus @@ t], FreeQ[t, # ] &]]]; Nest[f, {3}, 15] (* Ray Chandler, Jun 17 2006 *) CROSSREFS Cf. A120576, A120578, A120579. Sequence in context: A201653 A230765 A250306 * A104695 A233904 A292576 Adjacent sequences:  A120574 A120575 A120576 * A120578 A120579 A120580 KEYWORD nonn,tabf AUTHOR Leroy Quet, Jun 15 2006 EXTENSIONS Extended by Ray Chandler, Jun 17 2006 STATUS approved

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Last modified December 5 03:59 EST 2021. Contains 349530 sequences. (Running on oeis4.)