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A304491 Last or deepest exponent in the power-tower for n. 4
1, 2, 3, 2, 5, 6, 7, 3, 2, 10, 11, 12, 13, 14, 15, 2, 17, 18, 19, 20, 21, 22, 23, 24, 2, 26, 3, 28, 29, 30, 31, 5, 33, 34, 35, 2, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 2, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 6, 65, 66, 67, 68, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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_k).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A007916(A278028(n, A288636(n))).

EXAMPLE

We have 16 = 2^2^2, so a(16) = 2.

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

We have 81 = 3^2^2, so a(81) = 2.

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

MATHEMATICA

a[n_]:=If[n==1, 1, With[{g=GCD@@FactorInteger[n][[All, 2]]}, If[g==1, n, a[g]]]];

Array[a, 100]

PROG

(PARI) a(n)={my(t=n); while(t, n=t; t=ispower(t)); n} \\ Andrew Howroyd, Aug 26 2018

CROSSREFS

Cf. A052409, A052410, A007916, A089723, A164337, A277562, A277564, A278028, A288636, A289023, A294336, A294337, A304481, A304492, A304495.

Sequence in context: A259445 A080979 A287620 * A277803 A062789 A066069

Adjacent sequences:  A304488 A304489 A304490 * A304492 A304493 A304494

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 13 2018

STATUS

approved

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Last modified October 6 12:35 EDT 2022. Contains 357264 sequences. (Running on oeis4.)