A096309 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 ...).

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, 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, 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

Offset

1,4

Comments

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

Sequence A185102 is a (better?) variant, identical except for A185102(1)=0. - M. F. Hasler, Nov 21 2013

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A087049, A185102.

Sequence in context: A088737 A318434 A321455 * A185102 A049419 A299090

Adjacent sequences: A096306 A096307 A096308 * A096310 A096311 A096312

Keyword

easy,nonn

Author

Franz Vrabec, Jun 27 2004

Extensions

More terms from Jean-François Alcover, Nov 20 2013

Status

approved