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A057609
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Powers of a prime lucky number (A031157) but excluding lucky numbers (A000959).
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1
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27, 81, 243, 343, 1849, 2197, 2401, 4489, 5329, 6241, 6561, 16129, 16807, 19683, 22801, 26569, 28561, 37249, 44521, 49729, 58081, 59049, 79507, 80089, 94249, 109561, 117649, 134689, 177147, 177241, 187489, 214369, 237169, 361201, 371293, 375769, 383161, 389017
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OFFSET
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1,1
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COMMENTS
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Up to 10^7, terms are 3^3, 3^4, 3^5, 3^8, 3^9, 3^10, 3^11, 3^12, 3^13, 7^3, 7^4, 7^5, 7^6, 13^3, 13^4, 13^5, 13^6, 31^4, 43^2, 43^3, 43^4, 67^2, ..., . - Robert G. Wilson v, May 12 2006
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LINKS
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EXAMPLE
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In the first 23 terms of A000959, {1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99}, 3 is a prime lucky number (A031157), and 3^2 is also a lucky number, but 3^3=27 and 3^4=81 are not lucky numbers, so they are terms of this sequence.
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MATHEMATICA
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lst = Range[1, 2*10^6, 2]; i = 2; While[i <= (len = Length[lst]) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++ ]; m = Last@ lst; Complement[ Reap[ Do[ If[x^2 > m, Break[]]; If[PrimeQ[x], y = x^2; While[y <= m, Sow@ y; y *= x]], {x, lst}]] [[2, 1]], lst] (* Robert G. Wilson v, May 12 2006, corrected by Giovanni Resta, May 10 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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