A073843 a(1) = 1; for n > 1 a(n) = smallest number of the form n^r (with r rational != 1) not included earlier.

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

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. Adams-Watters, 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. Adams-Watters, 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^(b-1); fi; od:c[1]=1:seq(c[j], j=1..150);

Crossrefs

Cf. A073842.

Sequence in context: A277802 A159253 A011262 * A366423 A073842 A136271

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