A120576 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)=2.

2, 1, 3, 6, 4, 12, 7, 14, 28, 11, 77, 5, 15, 33, 55, 165, 73, 146, 219, 438, 9, 18, 657, 1314, 8, 16, 23, 24, 36, 46, 48, 69, 72, 92, 138, 144, 184, 207, 276, 368, 414, 552, 828, 1104, 1656, 3312, 1847, 12929, 5541, 9235, 27705, 19, 38, 3694, 35093, 70186, 487, 974

Offset

1,1

Comments

Is this sequence a permutation of the positive integers?

Length of rows varies widely, is often 1. Row 129 has 12236 terms. - Michael De Vlieger, Oct 03 2017

Links

Michael De Vlieger, Table of n, a(n) for n = 1..18474 (rows 1 <= n <= 129)

Michael De Vlieger, Lengths of rows of A120576 and relation to number of divisors of the sum of terms in all previous rows.

Example

Array begins:
2
1
3
6
4,12
7,14,28
Now these terms add up to 77. So row 7 is the divisors of 77 which do not occur earlier in the sequence. 1 and 7 occur in earlier rows, so row 7 is (11,77).
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 A120576.
.
   n  tau(k(n-1))    m   delta         k
  --------------------------------------
   1        2        2     0           2
   2        2        1     1           3
   3        2        1     1           6
   4        4        1     3          12
   5        6        2     4          28
   6        6        3     3          77
   7        4        2     2         165
   8        8        5     3         438
   9        8        4     4        1314
  10       12        4     8        3312
  11       30       22     8       12929
  12        4        2     2       27705
  13        8        3     5       70186
  14        8        5     3      179216
  15       20       10    10      541544
  16       16        8     8     1559024
  17       20       11     9     4603588
  18       24       17     7    13776209
  19        2        1     1    27552418
  20        4        1     3    55104836
  ...
(End)

Mathematica

f[t_] := Flatten[Append[t, Select[Divisors[Plus @@ t], FreeQ[t, # ] &]]]; Nest[f, {2}, 14] (* Ray Chandler, Jun 17 2006 *)

Crossrefs

Cf. A120577, A120578, A120579.

Sequence in context: A268182 A094339 A317788 * A063707 A205840 A171084

Adjacent sequences: A120573 A120574 A120575 * A120577 A120578 A120579

Keyword

nonn,tabf

Author

Leroy Quet, Jun 15 2006

Extensions

Extended by Ray Chandler, Jun 17 2006

Status

approved