A119763 Irregular array where row n is the positive integers which divide the sum of all previous rows. a(1,1)=1.

1, 1, 1, 2, 1, 5, 1, 11, 1, 23, 1, 47, 1, 5, 19, 95, 1, 5, 43, 215, 1, 479, 1, 7, 137, 959, 1, 2063, 1, 4127, 1, 5, 13, 65, 127, 635, 1651, 8255, 1, 83, 229, 19007, 1, 38327, 1, 5, 15331, 76655, 1, 137, 1231, 168647, 1, 13, 109, 239, 1417, 3107, 26051, 338663, 1, 19, 37277, 708263

Offset

1,4

Links

John Tyler Rascoe, Rows n = 1..100, flattened

Formula

a(n,k) | Sum_{j=1..n-1, l>=1} a(j,l). a(n,k) > a(n,k-1). a(n,1)=1. - R. J. Mathar, Jun 23 2006

Example

Array begins:
  1
  1
  1,2
  1,5
  1,11
  1,23
  1,47
  1,5,19,95
The sum of these terms is 215.
Since the divisors of 215 are 1, 5, 43 and 215, row 9 = (1,5,43,215).

Maple

A119763 := proc(nmax) local a, dvs; a := [1] ; while nops(a) < nmax do dvs := numtheory[divisors](sum('a[i]', i=1..nops(a))) ; a := [op(a), op(dvs) ] ; od ; end: a := A119763(200) ; for i from 1 to nops(a) do printf("%d, ", a[i]) ; od ; # R. J. Mathar, Jun 23 2006

Mathematica

Module[{arr={1}}, Do[AppendTo[arr, Divisors[Total[arr]]]; arr=Flatten[arr], {20}]; arr] (* Harvey P. Dale, May 27 2012 *)

Prog

(Scheme) ;; positive-divisors gives the list of divisors of n in decreasing order
(define (A119763 n seq)
(cond
[(= n 0) seq]
[else (A119763 (sub1 n) (append seq (reverse (positive-divisors (apply + seq)))))]))
(A119763 20 (list 1)) ;; Joshua Zucker, Jun 21 2006
(PARI)
A119763(row_max) = {my(s=1, v=List([[1]])); for(i=1, row_max-1, my(x=divisors(s)); listput(v, x); s+=vecsum(x)); Vec(v)} \\ John Tyler Rascoe, Nov 16 2025

Crossrefs

Cf. A027750, A119762, A119765.

Sequence in context: A054251 A386946 A163963 * A363087 A092142 A348497

Adjacent sequences: A119760 A119761 A119762 * A119764 A119765 A119766

Keyword

nonn,tabf

Author

Leroy Quet, Jun 18 2006

Extensions

More terms from Joshua Zucker and R. J. Mathar, Jun 21 2006

Status

approved