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A130897
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Numbers that are not exponentially squarefree.
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7
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16, 48, 80, 81, 112, 144, 162, 176, 208, 240, 256, 272, 304, 324, 336, 368, 400, 405, 432, 464, 496, 512, 528, 560, 567, 592, 624, 625, 648, 656, 688, 720, 752, 768, 784, 810, 816, 848, 880, 891, 912, 944, 976
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OFFSET
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1,1
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COMMENTS
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A positive integer is called exponentially squarefree (e-squarefree) if in its prime power factorization all the exponents are squarefree.
a(n) is the sequence of positive integers in which prime power factorization there is at least one nonsquarefree exponent.
n is non-e-squarefree iff f(n)=0, where f(n) is the exponential Moebius function A166234.
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LINKS
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M. V. Subbarao, On some arithmetic convolutions, in The Theory of Arithmetic Functions, Lecture Notes in Mathematics No. 251, 247-271, Springer, 1972, doi:10.1007/BFb0058796.
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EXAMPLE
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16=2^4, 48=2^4*3, 256=2^8 are non-e-squarefree, since 4 and 8 are nonsquarefree.
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MAPLE
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filter:=n -> not andmap(t -> numtheory:-issqrfree(t[2]), ifactors(n)[2]);
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MATHEMATICA
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Select[Range@ 1000, ! AllTrue[Last /@ FactorInteger@ #, SquareFreeQ] &] (* Michael De Vlieger, Sep 07 2015, Version 10 *)
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PROG
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(Haskell)
a130897 n = a130897_list !! (n-1)
a130897_list = filter
(any (== 0) . map (a008966 . fromIntegral) . a124010_row) [1..]
(PARI) is(n)=my(f=factor(n)[, 2]); for(i=1, #f, if(!issquarefree(f[i]), return(1))); 0 \\ Charles R Greathouse IV, Sep 03 2015
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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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