A120578 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)=4.

4, 1, 2, 7, 14, 28, 8, 56, 3, 5, 6, 10, 12, 15, 20, 24, 30, 40, 60, 120, 31, 93, 155, 465, 13, 39, 403, 1209, 17, 169, 221, 2873, 21, 293, 879, 2051, 6153, 25, 50, 311, 622, 1555, 3110, 7775, 15550, 37, 43, 74, 86, 148, 172, 259, 301, 518, 602, 1036, 1204, 1591

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:
  4
  1,2
  7
  14
  28
  8,56
Now these terms add up to 120. So row 7 is the divisors of 120 which do not occur earlier in the sequence. 1,2,4 and 8 occur in earlier rows, so row 7 is (3,5,6,10,12,15,20,24,30,40,60,120).

Mathematica

f[t_] := Flatten[Append[t, Select[Divisors[Plus @@ t], FreeQ[t, # ] &]]]; Nest[f, {4}, 12] (* Ray Chandler, Jun 17 2006 *)

Prog

(Python)
def A120578(rowmax):
    A = [4]
    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, A120579.

Sequence in context: A243584 A084460 A216863 * A096249 A081454 A133883

Adjacent sequences: A120575 A120576 A120577 * A120579 A120580 A120581

Keyword

nonn,look,tabf

Author

Leroy Quet, Jun 15 2006

Extensions

Extended by Ray Chandler, Jun 17 2006

Status

approved