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A304495 Decapitate the power-tower for n, i.e., remove the last (deepest) exponent. 4
0, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(1) = 0 by convention.

Let {c(i)} = A007916 denote the sequence of numbers > 1 which are not perfect powers. Every positive integer n has a unique representation as a tower n = c(x_1)^c(x_2)^c(x_3)^...^c(x_k), where the exponents are nested from the right. Then a(n) = c(x_1)^c(x_2)^c(x_3)^...^c(x_{k-1}).

LINKS

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

FORMULA

a(m) <> 1 if m is a perfect power (A001597). - Michel Marcus, Jul 23 2018

EXAMPLE

We have 64 = 2^6, so a(64) = 2.

We have 216 = 6^3, so a(216) = 6.

We have 256 = 2^2^3, so a(256) = 2^2 = 4.

MATHEMATICA

tow[n_]:=If[n==1, {}, With[{g=GCD@@FactorInteger[n][[All, 2]]}, If[g===1, {n}, Prepend[tow[g], n^(1/g)]]]];

Table[If[n==1, 0, Power@@Most[tow[n]]], {n, 100}]

PROG

(PARI) A304495(n) = if(1==n, 0, my(e, r, tow = List([])); while((e = ispower(n, , &r)) > 1, listput(tow, r); n = e; ); n = 1; while(length(tow)>0, e = tow[#tow]; listpop(tow); n = e^n; ); (n)); \\ Antti Karttunen, Jul 23 2018

CROSSREFS

Cf. A052409, A052410, A001597, A007916, A089723, A164337, A277562, A277564, A278028, A288636, A289023, A294336, A294337, A304481, A304491, A304492.

Sequence in context: A058393 A131256 A245562 * A175069 A245563 A122945

Adjacent sequences:  A304492 A304493 A304494 * A304496 A304497 A304498

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 13 2018

EXTENSIONS

Name edited and more terms from Antti Karttunen, Jul 23 2018

STATUS

approved

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Last modified January 24 19:03 EST 2022. Contains 350565 sequences. (Running on oeis4.)