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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(PARI) a(n)=A090636(n, 28)

Crossrefs

Cf. A090636, A090635.

Sequence in context: A232727 A232766 A230855 * A261113 A280649 A134657

Adjacent sequences: A090634 A090635 A090636 * A090638 A090639 A090640

Keyword

nonn

Author

N. J. A. Sloane, Dec 14 2003

Extensions

Edited by M. F. Hasler, Nov 27 2019

Status

approved