cp's OEIS Frontend

A053025 Number of iterations of the number of divisors function (A000005) required to reach a fixed point (1 or 2) when started at n!.

%I A053025 #20 Aug 17 2024 09:01:26
%S A053025 1,1,4,5,4,6,7,7,7,5,7,7,7,7,7,6,7,7,7,7,7,8,7,7,7,7,6,6,8,6,7,6,7,8,
%T A053025 6,8,7,5,7,6,8,6,6,8,8,8,8,8,8,6,8,8,8,8,8,8,8,8,8,8,7,8,7,8,7,8,8,8,
%U A053025 8,8,8,7,8,8,8,8,8,8,7,8,8,8,8,8,8,8,8,8,8,8,7,8,7,8,8,8,7,8,8,7,8,8,8,8,8
%N A053025 Number of iterations of the number of divisors function (A000005) required to reach a fixed point (1 or 2) when started at n!.
%H A053025 Amiram Eldar, <a href="/A053025/b053025.txt">Table of n, a(n) for n = 1..10000</a>
%F A053025 a(n) = A036459(A000142(n)) = A036459(n!).
%e A053025 For n = 108, a(108) = 9 because the sequence of iterates is {108!, 798687560466432000, 7920, 60, 12, 6, 4, 3, 2}, and its length is 9.
%t A053025 a[n_] := -1 + Length @ FixedPointList[DivisorSigma[0, #] &, n!]; Array[a, 100]  (* _Amiram Eldar_, Aug 17 2024 *)
%o A053025 (PARI) a(n) = {my(f = n!, c = 1); while(f > 2, f = numdiv(f); c++); c;} \\ _Amiram Eldar_, Aug 17 2024
%Y A053025 Cf. A000005, A036459, A000142.
%K A053025 nonn
%O A053025 1,3
%A A053025 _Labos Elemer_, Feb 24 2000