A090637 Trajectory of 28 under the map k -> A003415(k) (taking the arithmetic derivative).

28, 32, 80, 176, 368, 752, 1520, 3424, 8592, 20096, 70464, 235072, 705280, 3023616, 13223680, 55540736, 278539264, 1392697344, 9541095424, 58609614848, 410267320320, 3397142953984, 24143851798528, 176071227916288, 1232666139967488, 9523075842834432

Offset: 1

Author

N. J. A. Sloane, Dec 14 2003

Keywords

• nonn

Comments

Equals A090636 from a(2) = 32 = A090636(5) on. See there and A090635 for more.

Examples

			a(2) = 28' = (2^2*7)' = 28*(2/2 + 1/7) = 32.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A090636, A090635.

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 28, (t->
      t*add(i[2]/i[1], i=ifactors(t)[2]))(a(n-1)))
    end:
seq(a(n), n=1..31);  # Alois P. Heinz, Dec 02 2019

Mathematica

a[n_] := a[n] = If[n == 1, 28, Function[t, t*Sum[i[[2]]/i[[1]], {i, FactorInteger[t]}]][a[n-1]]];Table[a[n], {n, 1, 31}] (* Jean-François Alcover, Jan 13 2025, after Alois P. Heinz *)

PARI

a(n)=A090636(n,28)

Extensions

Edited by M. F. Hasler, Nov 27 2019