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.

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

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)

Michael De Vlieger, Lengths of rows and relation to number of divisors of the sum of terms in all previous rows.

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