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a(1) = 1; for n>1, a(n) = a(n-1)*b(n-1) + 1, where {b(k)} is the concatenated list of the ordered positive divisors of the terms of {a(k)}.
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%I #20 Jan 27 2024 10:34:21

%S 1,2,3,7,8,25,26,183,184,369,1477,11817,11818,59091,1477276,1477277,

%T 2954555,38409216,998639617,998639618,2995918855,182751050156,

%U 33443442178549,33443442178550,66886884357101,267547537428405

%N a(1) = 1; for n>1, a(n) = a(n-1)*b(n-1) + 1, where {b(k)} is the concatenated list of the ordered positive divisors of the terms of {a(k)}.

%e The list of positive divisors of the terms of {a(k)} is (sequence A129646) 1; 1,2; 1,3; 1,7; 1,2,4,8; .... The n-th term of {a(k)} is a(n-1)*A129646(n-1) +1.

%p aklist := [] ;

%p A129645 := proc(n)

%p option remember;

%p global aklist ;

%p local prev;

%p if n = 1 then

%p return 1;

%p else

%p prev := procname(n-1) ;

%p sort([op(numtheory[divisors](prev))]) ;

%p aklist := [op(aklist),op(%)] ;

%p return prev*op(n-1,aklist)+1 ;

%p end if;

%p end proc:

%p seq(A129645(n),n=1..26) ; # _R. J. Mathar_, Aug 24 2013

%t aklist = {};

%t a[n_] := a[n] = If[n == 1, 1, With[{prev = a[n-1]}, aklist = Join[aklist, Divisors[prev]]; prev*aklist[[n-1]]+1]];

%t Table[a[n], {n, 1, 26}] (* _Jean-François Alcover_, Jan 27 2024, after _R. J. Mathar_ *)

%Y Cf. A129646.

%K nonn

%O 1,2

%A _Leroy Quet_, Apr 25 2007

%E More terms from _Sean A. Irvine_, May 19 2010; corrected (based on the ordered lists of divisors) by _Franklin T. Adams-Watters_, Aug 24 2013