A332066 Number of positive integers whose n-th power is not the sum of distinct smaller positive n-th powers.
2, 6, 9, 32, 24, 30, 41, 83, 49, 62, 71, 83
Offset: 1
Examples
For n = 1, only s = 1 and s = 2 are not the sum of distinct smaller positive integers (to the power n = 1), for all s >= 3 on we have s^1 = 1^1 + (s-1)^1 with 1 and s-1 distinct positive integers. Thus a(1) = #{1, 2} = 2.
For n = 2, S2 = {1, 2, 3, 4, 6, 8} is the set of all s > 0 whose square is not the sum of distinct smaller squares, while 5^2 = 4^2 + 3^2, 7^2 = 6^2 + 3^2 + 2^2, and all s^2 >= 9^2 are also the sum of distinct smaller squares. Thus a(2) = #S2 = 6.
Formula
a(n) = lim_{k -> oo} A332065(n,k) - k.
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