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Numbers m such that the squarefree kernel of m is larger than the squarefree kernel of m+1.
2

%I #11 Aug 31 2020 02:40:29

%S 3,7,11,15,17,19,23,24,26,31,35,39,43,44,47,51,53,55,59,62,63,67,71,

%T 74,79,80,83,87,89,91,95,97,99,103,107,111,115,116,119,120,123,124,

%U 127,131,134,139,143,146,149,151,155,159,161,163,167,168,170,174,175,179,183

%N Numbers m such that the squarefree kernel of m is larger than the squarefree kernel of m+1.

%C The numbers of terms not exceeding 10^k for k = 1, 2, ... are 2, 33, 345, 3393, 33910, 338730, 3387053, 33868719, 338683700, 3386831527, ... Apparently the asymptotic density of this sequence is 0.33868... - _Amiram Eldar_, Aug 31 2020

%H Amiram Eldar, <a href="/A079710/b079710.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) is asymptotic to c*n where c=2.94...

%t rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; Select[Range[100], rad[#] > rad[# + 1] &] (* _Amiram Eldar_, Aug 31 2020 *)

%Y Complement of A079709.

%Y Cf. A007947 (squarefree kernel).

%K nonn

%O 1,1

%A _Benoit Cloitre_, Jan 31 2003