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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 ...). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)