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

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, 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, 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

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A036459(A000142(n)) = A036459(n!).

Example

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.

Mathematica

a[n_] := -1 + Length @ FixedPointList[DivisorSigma[0, #] &, n!]; Array[a, 100]  (* Amiram Eldar, Aug 17 2024 *)

Prog

(PARI) a(n) = {my(f = n!, c = 1); while(f > 2, f = numdiv(f); c++); c; } \\ Amiram Eldar, Aug 17 2024

Crossrefs

Cf. A000005, A036459, A000142.

Sequence in context: A248624 A363195 A085428 * A010664 A074967 A021877

Adjacent sequences: A053022 A053023 A053024 * A053026 A053027 A053028

Keyword

nonn

Author

Labos Elemer, Feb 24 2000

Status

approved