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A082097 a(n) = d(a(n-1)) + n = A000005(a(n-1)) + n, with a(1)=1.

%I A082097 #14 Mar 28 2024 16:34:48
%S A082097 1,1,1,5,7,8,11,10,13,12,17,14,17,16,20,22,21,22,23,22,25,25,26,28,31,
%T A082097 28,33,32,35,34,35,36,42,42,43,38,41,40,47,42,49,45,49,47,47,48,57,52,
%U A082097 55,54,59,54,61,56,63,62,61,60,71,62,65,66,71,66,73,68,73,70,77,74
%N A082097 a(n) = d(a(n-1)) + n = A000005(a(n-1)) + n, with a(1)=1.
%H A082097 G. C. Greubel, <a href="/A082097/b082097.txt">Table of n, a(n) for n = 1..10000</a>
%p A082097 with(numtheory);
%p A082097 a:= proc(n) option remember;
%p A082097    if n < 4 then 1
%p A082097    else tau(a(n-1)) + n
%p A082097    fi
%p A082097  end:
%p A082097 seq(a(n), n=1..70); # _G. C. Greubel_, Aug 31 2019
%t A082097 a[n_]:= If[n<4, 1, DivisorSigma[0, a[n-1]] + n]; Table[a[n], {n, 70}] (* modified by _G. C. Greubel_, Aug 31 2019 *)
%t A082097 nxt[{n_,a_}]:={n+1,DivisorSigma[0,a]+n+1}; Join[{1,1},NestList[nxt,{3,1},70][[;;,2]]] (* _Harvey P. Dale_, Mar 28 2024 *)
%o A082097 (PARI) a(n) = if(n<4,1, numdiv(a(n-1)) + n); \\ _G. C. Greubel_, Aug 31 2019
%o A082097 (Magma) a:= func< n | n lt 4 select 1 else n + NumberOfDivisors(Self(n-1)) >;
%o A082097 [a(n): n in [1..70]]; // _G. C. Greubel_, Aug 31 2019
%o A082097 (Sage)
%o A082097 def a(n):
%o A082097     if n<4: return 1
%o A082097     else: return sigma(a(n-1), 0) + n
%o A082097 [a(n) for n in (1..70)] # _G. C. Greubel_, Aug 31 2019
%o A082097 (GAP)
%o A082097 a:= function(n)
%o A082097     if n<4 then return 1;
%o A082097     else return Tau(a(n-1)) + n;
%o A082097     fi;
%o A082097   end;
%o A082097 List([1..70], n-> a(n) ); # _G. C. Greubel_, Aug 31 2019
%Y A082097 Cf. A069103, A082094, A082095, A082096.
%K A082097 nonn
%O A082097 1,4
%A A082097 _Labos Elemer_, Apr 11 2003