A119762 Irregular array where row n is the distinct primes which divide the sum of all previous rows. a(1)=2.

2, 2, 2, 2, 3, 11, 2, 11, 5, 7, 47, 2, 47, 11, 13, 167, 2, 167, 503, 2, 503, 1511, 2, 1511, 5, 907, 13, 419, 5879, 2, 5879, 31, 569, 13, 23, 61, 2, 3, 191, 2, 41, 113, 2, 73, 29, 647, 7, 2777, 71, 313, 13, 37, 47, 2, 3, 11, 43, 13, 17, 103, 2, 3, 53, 2, 23, 499, 2, 3, 7, 13, 43, 2

Offset

1,1

Links

Table of n, a(n) for n=1..72.

Formula

a(n,k) | sum{j=1..n-1,l=1,2,...} a(j,l). a(n,k) > a(n,k-1). a(n,k)=A000040(s) for some s. - R. J. Mathar, Jun 23 2006

Example

Array begins:
2
2
2
2,3
11
2,11
5,7
47
2,47
The sum of these terms is 143.
Since the distinct primes which divide 143 are 11 and 13, row 10 =(11,13).

Maple

A119762 := proc(nmax) local a, dvs, j; a := [2] ; while nops(a) < nmax do dvs := op(2, ifactors(sum('a[i]', i=1..nops(a)))) ; for j from 1 to nops(dvs) do a := [op(a), op(1, op(j, dvs))] ; od ; od ; end: a := A119762(200) : for i from 1 to nops(a) do printf("%d, ", a[i]) ; od ; # R. J. Mathar, Jun 23 2006

Prog

(PLT Scheme) ;; factorize is a prime-factorization routine that returns a list of (prime exponent) pairs for each factor.
(define (A119762 n seq)
(cond
[(= n 0) seq]
[else (A119762 (sub1 n) (append seq (map first (factorize (apply + seq)))))]))
(A119762 50 (list 2)) ;; - Joshua Zucker, Jun 21 2006

Crossrefs

Cf. A027748.

Sequence in context: A248780 A213021 A078228 * A153667 A216322 A335383

Adjacent sequences: A119759 A119760 A119761 * A119763 A119764 A119765

Keyword

nonn,tabf

Author

Leroy Quet, Jun 18 2006

Extensions

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

Status

approved