|
%I #27 Jan 05 2024 02:50:08
%S 0,0,0,1,0,0,0,2,1,0,0,1,0,0,0,3,0,1,0,1,0,0,0,2,1,0,2,1,0,0,0,4,0,0,
%T 0,1,0,0,0,2,0,0,0,1,1,0,0,3,1,1,0,1,0,2,0,2,0,0,0,1,0,0,1,5,0,0,0,1,
%U 0,0,0,2,0,0,1,1,0,0,0,3,3,0,0,1,0,0,0,2,0,1
%N a(n) = 0 if n is squarefree, otherwise 1 + a(n/rad(n)) where rad = A007947 (squarefree kernel).
%C This sequence is not the same as A046660.
%H Reinhard Zumkeller, <a href="/A066301/b066301.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A051903(n)-1 for n > 1, a(1) = 0.
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A033150 - 1 = 0.705211... . - _Amiram Eldar_, Jan 05 2024
%e a(24) = 1 + a(24/rad(24)) = 1 + a(24/6) = 1 + a(4) = 1 + (1+a(4/rad(4))) = 1 + (1+a(4/2)) = 2 + a(2) = 2 + 0 = 2.
%t a[n_] := Max[FactorInteger[n][[;;, 2]]] - 1; Array[a, 100] (* _Amiram Eldar_, Jan 05 2024 *)
%o (PARI) a(n)=if(n>1, vecmax(factor(n)[,2])-1, 0) \\ _Charles R Greathouse IV_, Jul 15 2013
%o (Haskell)
%o a066301 1 = 0
%o a066301 n = a051903 n - 1 -- _Reinhard Zumkeller_, Jul 23 2013
%Y Cf. A005117, A007947, A003557, A008966, A033150, A046660, A051903.
%K nonn,easy
%O 1,8
%A _Reinhard Zumkeller_, Jan 01 2002
|
