A082097 - OEIS

%I #14 Mar 28 2024 16:34:48

%S 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 28,33,32,35,34,35,36,42,42,43,38,41,40,47,42,49,45,49,47,47,48,57,52,

%U 55,54,59,54,61,56,63,62,61,60,71,62,65,66,71,66,73,68,73,70,77,74

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

%H G. C. Greubel, <a href="/A082097/b082097.txt">Table of n, a(n) for n = 1..10000</a>

%p with(numtheory);

%p a:= proc(n) option remember;

%p    if n < 4 then 1

%p    else tau(a(n-1)) + n

%p    fi

%p  end:

%p seq(a(n), n=1..70); # _G. C. Greubel_, Aug 31 2019

%t 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 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 (PARI) a(n) = if(n<4,1, numdiv(a(n-1)) + n); \\ _G. C. Greubel_, Aug 31 2019

%o (Magma) a:= func< n | n lt 4 select 1 else n + NumberOfDivisors(Self(n-1)) >;

%o [a(n): n in [1..70]]; // _G. C. Greubel_, Aug 31 2019

%o (Sage)

%o def a(n):

%o     if n<4: return 1

%o     else: return sigma(a(n-1), 0) + n

%o [a(n) for n in (1..70)] # _G. C. Greubel_, Aug 31 2019

%o (GAP)

%o a:= function(n)

%o     if n<4 then return 1;

%o     else return Tau(a(n-1)) + n;

%o     fi;

%o   end;

%o List([1..70], n-> a(n) ); # _G. C. Greubel_, Aug 31 2019

%Y Cf. A069103, A082094, A082095, A082096.

%K nonn

%O 1,4

%A _Labos Elemer_, Apr 11 2003