

A304492


Position in the sequence of numbers that are not perfect powers (A007916) of the last or deepest exponent in the powertower 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
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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



