A120579 - OEIS

%I #21 Jan 10 2025 17:44:36

%S 5,1,2,3,6,17,34,4,68,7,10,14,20,28,35,70,140,8,16,29,58,116,232,464,

%T 19,73,1387,1433,2866,7165,14330,5732,28660,11,22,44,15763,31526,

%U 63052,38,55,83,95,110,166,190,209,415,418,830,913,1045,1577,1826,2090,3154,4565

%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)=5.

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

%H John Tyler Rascoe, <a href="/A120579/b120579.txt">Rows n = 1..100, flattened</a>

%e Array begins:

%e   5

%e   1

%e   2,3,6

%e   17

%e   34

%e 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).

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

%o (Python)

%o def A120579(rowmax):

%o     A = [5]

%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, A120578.

%K nonn,look,tabf

%O 1,1

%A _Leroy Quet_, Jun 15 2006

%E Extended by _Ray Chandler_, Jun 17 2006