A120579 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)=5.

5, 1, 2, 3, 6, 17, 34, 4, 68, 7, 10, 14, 20, 28, 35, 70, 140, 8, 16, 29, 58, 116, 232, 464, 19, 73, 1387, 1433, 2866, 7165, 14330, 5732, 28660, 11, 22, 44, 15763, 31526, 63052, 38, 55, 83, 95, 110, 166, 190, 209, 415, 418, 830, 913, 1045, 1577, 1826, 2090, 3154, 4565

Offset

1,1

Comments

Is this sequence a permutation of the positive integers?

Links

John Tyler Rascoe, Rows n = 1..100, flattened

Example

Array begins:
  5
  1
  2,3,6
  17
  34
Now these terms add up to 68. So row 6 is the divisors of 68 which do not occur earlier in the sequence. 1, 2, 17 and 34 occur in earlier rows, so row 6 is (4,68).

Mathematica

f[t_] := Flatten[Append[t, Select[Divisors[Plus @@ t], FreeQ[t, # ] &]]]; Nest[f, {5}, 14] (* Ray Chandler, Jun 17 2006 *)

Prog

(Python)
def A120579(rowmax):
    A = [5]
    for n in range(2, rowmax+1):
        A.extend(k for k in divisors(sum(A)) if k not in A)
    return A # John Tyler Rascoe, Jan 10 2025

Crossrefs

Cf. A120576, A120577, A120578.

Sequence in context: A222214 A055185 A281409 * A093316 A085758 A154529

Adjacent sequences: A120576 A120577 A120578 * A120580 A120581 A120582

Keyword

nonn,look,tabf,changed

Author

Leroy Quet, Jun 15 2006

Extensions

Extended by Ray Chandler, Jun 17 2006

Status

approved