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%I #13 Jul 19 2016 11:08:39
%S 2,2,2,2,3,11,2,11,5,7,47,2,47,11,13,167,2,167,503,2,503,1511,2,1511,
%T 5,907,13,419,5879,2,5879,31,569,13,23,61,2,3,191,2,41,113,2,73,29,
%U 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
%N Irregular array where row n is the distinct primes which divide the sum of all previous rows. a(1)=2.
%F 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
%e Array begins:
%e 2
%e 2
%e 2
%e 2,3
%e 11
%e 2,11
%e 5,7
%e 47
%e 2,47
%e The sum of these terms is 143.
%e Since the distinct primes which divide 143 are 11 and 13, row 10 =(11,13).
%p 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
%o (PLT Scheme) ;;factorize is a prime-factorization routine that returns a list of (prime exponent) pairs for each factor.
%o (define (A119762 n seq)
%o (cond
%o [(= n 0) seq]
%o [else (A119762 (sub1 n) (append seq (map first (factorize (apply + seq)))))]))
%o (A119762 50 (list 2)) ;; - _Joshua Zucker_, Jun 21 2006
%Y Cf. A027748.
%K nonn,tabf
%O 1,1
%A _Leroy Quet_, Jun 18 2006
%E More terms from _Joshua Zucker_ and _R. J. Mathar_, Jun 21 2006
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