A096309 - OEIS

%I #14 Nov 18 2017 20:59:36

%S 1,1,1,2,1,1,1,2,2,1,1,2,1,1,1,3,1,2,1,2,1,1,1,2,2,1,2,2,1,1,1,2,1,1,

%T 1,2,1,1,1,2,1,1,1,2,2,1,1,3,2,2,1,2,1,2,1,2,1,1,1,2,1,1,2,2,1,1,1,2,

%U 1,1,1,2,1,1,2,2,1,1,1,3,3,1,1,2,1,1,1,2,1,2,1,2,1,1,1,2,1,2,2,2

%N a(1)=1; for n > 1, a(n) is the number of levels in the "stacked" prime number factorization of n (prime number factorization of the exponents if necessary and so on ...).

%C For n > 1: a(n)=1 iff n squarefree.

%C Sequence A185102 is a (better?) variant, identical except for A185102(1)=0. - _M. F. Hasler_, Nov 21 2013

%H Antti Karttunen, <a href="/A096309/b096309.txt">Table of n, a(n) for n = 1..65537</a>

%e a(4)=2 because 4=2^2; a(8)=2 because 8=2^3; a(16)=3 because 16=2^(2^2).

%e a(65536) = a(2^2^2^2) = a(2^^4) = 4 is the first term larger than 3; the index of the first a(n) > 4, n = 2^^5, has 19729 digits. - _M. F. Hasler_, Nov 21 2013

%t f[n_Integer] := FactorInteger[n][[All, 2]]; a[n_] := Depth[f[n] //. k_Integer /; k > 1 :> f[k]] - 1; Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Nov 20 2013 *)

%o (PARI) A096309=n->if(n>1,vecmax(apply(a,factor(n)[,2])))+1 \\ _M. F. Hasler_, Nov 21 2013

%Y Cf. A087049, A185102.

%K easy,nonn

%O 1,4

%A _Franz Vrabec_, Jun 27 2004

%E More terms from _Jean-François Alcover_, Nov 20 2013