A377643 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.

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, 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, 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

Offset: 1

Author

Rafik Khalfi, Nov 03 2024

Keywords

• nonn

Examples

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

Crossrefs

Cf. A001414 (sopfr).

Programs

Maple

f := proc(n)
  add(op(1, i) * op(2, i), i = ifactors(n)[2]):
end proc:
g := proc(n)
  2 + f(n):
end proc:
A377643 := proc(n)
local k, result:
 k := 1:
result := n:
while result <> 8 do
result := g(result):
k := k + 1:
end do:
k:
end proc:
A377643(8) := 1:
map(A377643, [$1..100]);

Mathematica

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 *)