%I #13 Oct 31 2019 11:55:37
%S 1,3,4,8,9,2,5,17,15,36,21,7,16,25,27,20,40,33,35,19,18,39,41,43,28,
%T 64,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,47,121,87,89,
%U 23,68,93,95,97,99,101,103,105,107,109,100,11,113,115,117,119,244,125,127,129
%N a(n) is the smallest positive integer not occurring earlier in the sequence such that sum{k=1 to n} a(k) = j^r, j = any positive integer, r = any integer >= 2.
%C Is this sequence a permutation of the positive integers?
%e The sum of the first 7 terms of the sequence is 32. 17 is the smallest positive integer m that does not occur earlier in the sequence and is such that 32+m is of the form j^r, r >=2. So a(8) = 17 and the sum of the first 8 terms of the sequence is 49 = 7^2.
%t f[n_] := n == 1 || GCD @@ Last /@ FactorInteger[n] > 1;g[l_List] := Block[{k = 1, s = Plus @@ l},While[MemberQ[l, k] || ! f[s + k], k++ ];Append[l, k]];Nest[g, {}, 70] (* _Ray Chandler_, Jan 23 2007 *)
%Y Cf. A001597.
%K nonn
%O 1,2
%A _Leroy Quet_, Jan 13 2007
%E Extended by _Ray Chandler_, Jan 23 2007
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