A120577 - OEIS

%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