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%I #8 Jun 03 2023 07:26:45
%S 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,
%T 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,
%U 2,3,2,2,2,2,2,2,2,2,1,1,3,2,2,3,2,3,3
%N The number of distinct primorial numbers (A002110) larger than 1 in the representation of A025487(n) as a product of primorial numbers.
%C The number of distinct exponents in the prime factorization of A025487(n).
%C The minimal number of powers of primorial numbers (A100778) in the representation of A025487(n) as a product of powers of primorial numbers.
%C 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).
%H Amiram Eldar, <a href="/A363455/b363455.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A071625(A025487(n)).
%t 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
%Y Cf. A002110, A006939, A025487, A051282, A071625, A100778, A304886, A363456.
%K nonn
%O 1,6
%A _Amiram Eldar_, Jun 03 2023
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