

A073843


a(1) = 1; for n > 1 a(n) = smallest number of the form n^r (with r rational != 1) not included earlier.


1



1, 4, 9, 2, 25, 36, 49, 16, 3, 100, 121, 144, 169, 196, 225, 8, 289, 324, 361, 400, 441, 484, 529, 576, 5, 676, 81, 784, 841, 900, 961, 64, 1089, 1156, 1225, 6, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 7, 2500, 2601, 2704
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OFFSET

1,2


COMMENTS

The formula in terms of A052409 and A052410 implies that the sequence is a permutation of the positive integers.  Franklin T. AdamsWatters, Jul 26 2006


LINKS

Table of n, a(n) for n=1..52.


FORMULA

a(n) = n^((b  (1)^b) / b), b = gcd(b_1, ..., b_r) with prime factorization n = p_1^b_1*...*p_r^b_r.  Sascha Kurz, Aug 14 2002
If A052409(n) is odd, a(n) = A052410(n)^(A052409(n) + 1); otherwise a(n) = A052410(n)^(A052409(n)  1).  Franklin T. AdamsWatters, Jul 26 2006


EXAMPLE

a(15) = 15^2 = 225, but a(16) = 8 = 16^(3/4).


MAPLE

for n from 2 to 150 do a := ifactors(n); b := a[2][1][2]:for j from 2 to nops(a[2]) do b := gcd(b, a[2][j][2]); od; bb := floor(evalf(n^(1/b))); if(b mod 2=1) then c[n] := bb^(b+1) else c[n] := bb^(b1); fi; od:c[1]=1:seq(c[j], j=1..150);


CROSSREFS

Cf. A073842.
Sequence in context: A277802 A159253 A011262 * A073842 A136271 A113970
Adjacent sequences: A073840 A073841 A073842 * A073844 A073845 A073846


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Aug 13 2002


EXTENSIONS

More terms from Sascha Kurz, Aug 14 2002


STATUS

approved



