login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A120577 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. 4
3, 1, 2, 4, 5, 10, 25, 50, 20, 100, 11, 22, 44, 55, 110, 220, 31, 62, 341, 682, 29, 58, 899, 1798, 79, 158, 2291, 4582, 37, 74, 148, 316, 2923, 5846, 11692, 8, 4091, 8182, 16364, 32728, 7, 21, 4481, 13443, 31367, 94101, 23, 449, 529, 10327, 237521, 17, 34, 85, 170 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Is this sequence a permutation of the positive integers?

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..12111 (rows 1 <= n <= 177)

Michael De Vlieger, Lengths of rows and relation to number of divisors of the sum of terms in all previous rows.

EXAMPLE

Array begins:

   3

   1

   2,  4

   5, 10

  25

  50

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).

From Michael De Vlieger, Oct 03 2017: (Start)

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

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

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

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

.

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

   ----------------------------------------

   1        -        3      -             3

   2        2        1      1             4

   3        3        2      1            10

   4        4        2      2            25

   5        3        1      2            50

   6        6        1      5           100

   7        9        2      7           220

   8       12        6      6           682

   9        8        4      4          1798

  10        8        4      4          4582

  11        8        4      4         11692

  12       12        7      5         32728

  13        8        5      3         94101

  14        8        6      2        237521

  15        6        5      1        486370

  16       16       12      4       1413640

  17       32       25      7       4653590

  18       16       11      5      13394637

  19       12       10      2      33108197

  20        8        6      2      69019691

  ...

  (End)

MATHEMATICA

f[t_] := Flatten[Append[t, Select[Divisors[Plus @@ t], FreeQ[t, # ] &]]]; Nest[f, {3}, 15] (* Ray Chandler, Jun 17 2006 *)

CROSSREFS

Cf. A120576, A120578, A120579.

Sequence in context: A201653 A230765 A250306 * A104695 A233904 A292576

Adjacent sequences:  A120574 A120575 A120576 * A120578 A120579 A120580

KEYWORD

nonn,tabf

AUTHOR

Leroy Quet, Jun 15 2006

EXTENSIONS

Extended by Ray Chandler, Jun 17 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 03:59 EST 2021. Contains 349530 sequences. (Running on oeis4.)