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%I #18 Oct 11 2017 05:22:23
%S 3,1,2,4,5,10,25,50,20,100,11,22,44,55,110,220,31,62,341,682,29,58,
%T 899,1798,79,158,2291,4582,37,74,148,316,2923,5846,11692,8,4091,8182,
%U 16364,32728,7,21,4481,13443,31367,94101,23,449,529,10327,237521,17,34,85,170
%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)=3.
%C Is this sequence a permutation of the positive integers?
%H Michael De Vlieger, <a href="/A120577/b120577.txt">Table of n, a(n) for n = 1..12111</a> (rows 1 <= n <= 177)
%H Michael De Vlieger, <a href="/A120577/a120577.txt">Lengths of rows and relation to number of divisors of the sum of terms in all previous rows.</a>
%e Array begins:
%e 3
%e 1
%e 2, 4
%e 5, 10
%e 25
%e 50
%e Now these terms add up to 100. So row 7 is the divisors of 100 which do not occur earlier in the sequence. 1,2,4,5,10,25 and 50 occur in earlier rows, so row 7 is (20,100).
%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 this sequence.
%e .
%e n tau(k(n-1)) m delta k
%e ----------------------------------------
%e 1 - 3 - 3
%e 2 2 1 1 4
%e 3 3 2 1 10
%e 4 4 2 2 25
%e 5 3 1 2 50
%e 6 6 1 5 100
%e 7 9 2 7 220
%e 8 12 6 6 682
%e 9 8 4 4 1798
%e 10 8 4 4 4582
%e 11 8 4 4 11692
%e 12 12 7 5 32728
%e 13 8 5 3 94101
%e 14 8 6 2 237521
%e 15 6 5 1 486370
%e 16 16 12 4 1413640
%e 17 32 25 7 4653590
%e 18 16 11 5 13394637
%e 19 12 10 2 33108197
%e 20 8 6 2 69019691
%e ...
%e (End)
%t f[t_] := Flatten[Append[t, Select[Divisors[Plus @@ t], FreeQ[t, # ] &]]]; Nest[f, {3}, 15] (* _Ray Chandler_, Jun 17 2006 *)
%Y Cf. A120576, A120578, A120579.
%K nonn,tabf
%O 1,1
%A _Leroy Quet_, Jun 15 2006
%E Extended by _Ray Chandler_, Jun 17 2006
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