A125219 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.

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, 64, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 47, 121, 87, 89, 23, 68, 93, 95, 97, 99, 101, 103, 105, 107, 109, 100, 11, 113, 115, 117, 119, 244, 125, 127, 129

Offset

1,2

Comments

Is this sequence a permutation of the positive integers?

Links

Table of n, a(n) for n=1..68.

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A001597.

Sequence in context: A322117 A181778 A245026 * A075562 A316137 A089290

Adjacent sequences: A125216 A125217 A125218 * A125220 A125221 A125222

Keyword

nonn

Author

Leroy Quet, Jan 13 2007

Extensions

Extended by Ray Chandler, Jan 23 2007

Status

approved