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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

%I #21 Jan 10 2025 17:43:20

%S 4,1,2,7,14,28,8,56,3,5,6,10,12,15,20,24,30,40,60,120,31,93,155,465,

%T 13,39,403,1209,17,169,221,2873,21,293,879,2051,6153,25,50,311,622,

%U 1555,3110,7775,15550,37,43,74,86,148,172,259,301,518,602,1036,1204,1591

%N 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.

%C Is this sequence a permutation of the positive integers?

%H John Tyler Rascoe, <a href="/A120578/b120578.txt">Rows n = 1..100, flattened</a>

%e Array begins:

%e 4

%e 1,2

%e 7

%e 14

%e 28

%e 8,56

%e 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).

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

%o (Python)

%o def A120578(rowmax):

%o A = [4]

%o for n in range(2,rowmax+1):

%o A.extend(k for k in divisors(sum(A)) if k not in A)

%o return A # _John Tyler Rascoe_, Jan 10 2025

%Y Cf. A120576, A120577, A120579.

%K nonn,look,tabf

%O 1,1

%A _Leroy Quet_, Jun 15 2006

%E Extended by _Ray Chandler_, Jun 17 2006