A377643 - OEIS

%I #14 Nov 24 2024 09:56:26

%S 7,6,5,5,4,4,3,1,2,3,6,3,5,7,4,4,6,4,5,7,4,5,5,7,4,7,7,6,7,4,6,4,5,5,

%T 8,4,6,6,5,6,8,8,7,7,6,8,6,6,5,8,6,6,6,6,5,5,8,6,7,8,6,9,5,8,8,5,8,6,

%U 7,5,7,8,6,9,5,5,8,8,9,5,8,7,9,5,8,7,6,6,7,5,6,8,5,7,8,5,7,5,6,5

%N a(n) is the number of terms in the trajectory when the map x -> 2+sopfr(x) is iterated, starting from x = n until x = 8, with sopfr = A001414.

%e For n=1, the trajectory from n down to 8 comprises a(1) = 7 terms: 1 -> 2 -> 4 -> 6 -> 7 -> 9 -> 8.

%p f := proc(n)

%p   add(op(1, i) * op(2, i), i = ifactors(n)[2]):

%p end proc:

%p g := proc(n)

%p   2 + f(n):

%p end proc:

%p A377643 := proc(n)

%p local k, result:

%p  k := 1:

%p result := n:

%p while result <> 8 do

%p result := g(result):

%p k := k + 1:

%p end do:

%p k:

%p end proc:

%p A377643(8) := 1:

%p map(A377643, [$1..100]);

%t s[n_] := 2 + Plus @@ Times @@@ FactorInteger[n]; s[1] = 2; a[n_] := Length@ NestWhileList[s, n, # != 8 &]; Array[a, 100] (* _Amiram Eldar_, Nov 07 2024 *)

%Y Cf. A001414 (sopfr).

%K nonn

%O 1,1

%A _Rafik Khalfi_, Nov 03 2024