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A304492 Position in the sequence of numbers that are not perfect powers (A007916) of the last or deepest exponent in the power-tower for n. 3
1, 2, 3, 2, 4, 5, 6, 3, 2, 7, 8, 9, 10, 11, 12, 2, 13, 14, 15, 16, 17, 18, 19, 20, 2, 21, 3, 22, 23, 24, 25, 4, 26, 27, 28, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 2, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 5, 55, 56, 57, 58, 59, 60 (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) = x_k.

LINKS

Table of n, a(n) for n=1..70.

FORMULA

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

MATHEMATICA

nn=100;

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

rads=Union[Array[a, nn]];

Table[a[n], {n, nn}]/.Table[rads[[i]]->i, {i, Length[rads]}]

CROSSREFS

Cf. A052409, A052410, A007916, A089723, A164337, A277562, A277564, A278028, A288636, A289023, A294336, A294337, A304481, A304491, A304495.

Sequence in context: A325810 A324400 A297157 * A305303 A304757 A140503

Adjacent sequences:  A304489 A304490 A304491 * A304493 A304494 A304495

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 13 2018

STATUS

approved

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Last modified May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)