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

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, 28, 33, 32, 35, 34, 35, 36, 42, 42, 43, 38, 41, 40, 47, 42, 49, 45, 49, 47, 47, 48, 57, 52, 55, 54, 59, 54, 61, 56, 63, 62, 61, 60, 71, 62, 65, 66, 71, 66, 73, 68, 73, 70, 77, 74

Offset: 1

Author

Labos Elemer, Apr 11 2003

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A069103, A082094, A082095, A082096.

Programs

GAP

a:= function(n)
    if n<4 then return 1;
    else return Tau(a(n-1)) + n;
    fi;
  end;
List([1..70], n-> a(n) ); # G. C. Greubel, Aug 31 2019

Magma

a:= func< n | n lt 4 select 1 else n + NumberOfDivisors(Self(n-1)) >;
[a(n): n in [1..70]]; // G. C. Greubel, Aug 31 2019

Maple

with(numtheory);
a:= proc(n) option remember;
   if n < 4 then 1
   else tau(a(n-1)) + n
   fi
 end:
seq(a(n), n=1..70); # G. C. Greubel, Aug 31 2019

Mathematica

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 *)
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 *)

PARI

a(n) = if(n<4,1, numdiv(a(n-1)) + n); \\ G. C. Greubel, Aug 31 2019

Sage

def a(n):
    if n<4: return 1
    else: return sigma(a(n-1), 0) + n
[a(n) for n in (1..70)] # G. C. Greubel, Aug 31 2019