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

%I

%S 1,4,9,2,25,36,49,16,3,100,121,144,169,196,225,8,289,324,361,400,441,

%T 484,529,576,5,676,81,784,841,900,961,64,1089,1156,1225,6,1369,1444,

%U 1521,1600,1681,1764,1849,1936,2025,2116,2209,2304,7,2500,2601,2704

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

%C 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

%F 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

%F 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

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

%p 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);

%Y Cf. A073842.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Aug 13 2002

%E More terms from _Sascha Kurz_, Aug 14 2002

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Last modified April 22 07:26 EDT 2021. Contains 343163 sequences. (Running on oeis4.)