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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)=2.
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%I #16 Oct 03 2017 20:55:36

%S 2,1,3,6,4,12,7,14,28,11,77,5,15,33,55,165,73,146,219,438,9,18,657,

%T 1314,8,16,23,24,36,46,48,69,72,92,138,144,184,207,276,368,414,552,

%U 828,1104,1656,3312,1847,12929,5541,9235,27705,19,38,3694,35093,70186,487,974

%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)=2.

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

%C Length of rows varies widely, is often 1. Row 129 has 12236 terms. - _Michael De Vlieger_, Oct 03 2017

%H Michael De Vlieger, <a href="/A120576/b120576.txt">Table of n, a(n) for n = 1..18474</a> (rows 1 <= n <= 129)

%H Michael De Vlieger, <a href="/A120576/a120576.txt">Lengths of rows of A120576 and relation to number of divisors of the sum of terms in all previous rows.</a>

%e Array begins:

%e 2

%e 1

%e 3

%e 6

%e 4,12

%e 7,14,28

%e 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).

%e From _Michael De Vlieger_, Oct 03 2017: (Start)

%e Lengths of rows of a(n) and relation to number of divisors of the sum of terms in all previous rows.

%e Key: n = index; m = length of row n; k = sum of the terms in all previous rows.

%e tau(k(n-1)) = number of divisors of k of the previous row.

%e delta = tau(k(n-1)) - m: i.e., divisors of k(n - 1) not in row n of A120576.

%e .

%e n tau(k(n-1)) m delta k

%e --------------------------------------

%e 1 2 2 0 2

%e 2 2 1 1 3

%e 3 2 1 1 6

%e 4 4 1 3 12

%e 5 6 2 4 28

%e 6 6 3 3 77

%e 7 4 2 2 165

%e 8 8 5 3 438

%e 9 8 4 4 1314

%e 10 12 4 8 3312

%e 11 30 22 8 12929

%e 12 4 2 2 27705

%e 13 8 3 5 70186

%e 14 8 5 3 179216

%e 15 20 10 10 541544

%e 16 16 8 8 1559024

%e 17 20 11 9 4603588

%e 18 24 17 7 13776209

%e 19 2 1 1 27552418

%e 20 4 1 3 55104836

%e ...

%e (End)

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

%Y Cf. A120577, A120578, A120579.

%K nonn,tabf

%O 1,1

%A _Leroy Quet_, Jun 15 2006

%E Extended by _Ray Chandler_, Jun 17 2006