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A242031
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Numbers n such that prime factorization n = p_1^k_1*p_2^k_2*...*p_r^k_r satisfies k_1 >= k_2 >= ... >= k_r.
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19
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72
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OFFSET
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1,2
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COMMENTS
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Complement sequence begins 18, 50, 54, 75, 90, 98, ... (A071365).
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LINKS
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EXAMPLE
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12 = 2^2*3^1 is in the sequence, but 18 = 2^1*3^2 is not.
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MAPLE
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filter:= proc(n)
local F;
F:= ifactors(n)[2];
F:= sort(F, (s, t) -> s[1]>t[1]);
ListTools:-Sorted(map(t -> t[2], F));
end:
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MATHEMATICA
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Select[Range[100], GreaterEqual @@ (FactorInteger[#][[All, 2]]) &]
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PROG
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(PARI) s=[]; for(n=1, 10^3, m=factor(n)[, 2]; if(vecsort(m, , 4)==m, s=concat(s, n))); s \\ Jens Kruse Andersen, Aug 18 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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