OFFSET
1,1
COMMENTS
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.
The density of {a(n)} is 0.04407699... (see comment in A209061). - Peter J. C. Moses and Vladimir Shevelev, Sep 08 2015
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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.
Laszlo Toth, On certain arithmetic functions involving exponential divisors, II., Annales Univ. Sci. Budapest., Sect. Comp., 27 (2007), 155-166.
EXAMPLE
16=2^4, 48=2^4*3, 256=2^8 are non-e-squarefree, since 4 and 8 are nonsquarefree.
MAPLE
filter:=n -> not andmap(t -> numtheory:-issqrfree(t[2]), ifactors(n)[2]);
select(filter, [$1..1000]); # Robert Israel, Sep 03 2015
MATHEMATICA
Select[Range@ 1000, ! AllTrue[Last /@ FactorInteger@ #, SquareFreeQ] &] (* Michael De Vlieger, Sep 07 2015, Version 10 *)
PROG
(Haskell)
a130897 n = a130897_list !! (n-1)
a130897_list = filter
(any (== 0) . map (a008966 . fromIntegral) . a124010_row) [1..]
-- Reinhard Zumkeller, Mar 13 2012
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Laszlo Toth, Mar 18 2011
STATUS
approved