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A048104
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If n = Product p_i^e_i (e_i >= 1) then for some i, p_i > e_i and for some j, p_j < e_j.
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3
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24, 40, 48, 56, 72, 80, 88, 96, 104, 112, 120, 136, 144, 152, 160, 162, 168, 176, 184, 192, 200, 208, 224, 232, 240, 248, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 405, 408, 416, 424, 440, 448, 456, 464, 472
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OFFSET
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1,1
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COMMENTS
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The asymptotic density of this sequence is 1 - Product_{p prime} (1-1/p^(p+1)) = 0.13585792767780221591... . - Amiram Eldar, Feb 14 2023
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LINKS
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EXAMPLE
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48 = 2^4*3^1 is a term but 12 = 2^2*3^1 is not.
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MATHEMATICA
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Select[Range[500], AnyTrue[(f = FactorInteger[#]), First[#1] > Last[#1] &] && AnyTrue[f, First[#1] < Last[#1] &] &] (* Amiram Eldar, Nov 13 2020 *)
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PROG
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(PARI) isok(n) = my(f=factor(n), b1=0, b2=0); for (i=1, #f~, if (f[i, 1] < f[i, 2], b1=1, if (f[i, 1] > f[i, 2], b2=1))); return(b1 && b2); \\ Michel Marcus, Nov 13 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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