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.

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

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