A134488 a(0)=1. a(n) = n + d(a(n-1)), where d(m) is the number of positive divisors of m.

1, 2, 4, 6, 8, 9, 9, 10, 12, 15, 14, 15, 16, 18, 20, 21, 20, 23, 20, 25, 23, 23, 24, 31, 26, 29, 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

0,2

Comments

Giving the sequence an offset of 1 instead and letting a(1)=1, we get the sequence beginning: 1,3,5,6,9,9,10,12,15,14,15,16,18,20,... This is the same sequence for every term from a(5) on.

Links

Table of n, a(n) for n=0..70.

Example

a(10)=14 because a(9) (=15) has 4 positive divisors (1,3,5,15) and then a(10)=10+4=14.

Maple

with(numtheory): a[0]:=1: for n to 60 do a[n]:=n+tau(a[n-1]) end do: seq(a[n], n=0..60); # Emeric Deutsch, Nov 12 2007

Mathematica

a = {1}; Do[AppendTo[a, Length[a] + Length[Divisors[a[[ -1]]]]], {70}]; a (* Stefan Steinerberger, Oct 30 2007 *)

Crossrefs

Cf. A000005.

Sequence in context: A087671 A088308 A167832 * A263800 A168496 A328077

Adjacent sequences: A134485 A134486 A134487 * A134489 A134490 A134491

Keyword

nonn

Author

Leroy Quet, Oct 28 2007

Extensions

More terms from Stefan Steinerberger, Oct 30 2007

Status

approved