A363455 The number of distinct primorial numbers (A002110) larger than 1 in the representation of A025487(n) as a product of primorial numbers.

0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 3, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 1, 3, 2, 1, 3, 2, 3, 2, 2, 2, 2, 2, 1, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 3, 2, 2, 3, 2, 3, 3

Offset: 1

Author

Amiram Eldar, Jun 03 2023

Keywords

• nonn

Comments

The number of distinct exponents in the prime factorization of A025487(n).

The minimal number of powers of primorial numbers (A100778) in the representation of A025487(n) as a product of powers of primorial numbers.

The record values are all the nonnegative integers. The positions of the records are the positions of the terms of the Chernoff sequence (A006939) in A025487, i.e., the first position of k, for k = 0, 1, 2, ..., is A363456(k).

Links

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

Crossrefs

Cf. A002110, A006939, A025487, A051282, A071625, A100778, A304886, A363456.

Programs

Mathematica

e[1] = 0; e[n_] := Length[Union[FactorInteger[n][[;; , 2]]]]; s = {0}; Do[If[GreaterEqual @@ (f = FactorInteger[n])[[;; , 2]] && PrimePi[f[[-1, 1]]] == Length[f], AppendTo[s, e[n]]], {n, 2, 10000}]; s

Formula

a(n) = A071625(A025487(n)).