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A361176
Numbers that are not exponentially cubefree: numbers with at least one noncubefree exponent in their canonical prime factorization.
1
256, 768, 1280, 1792, 2304, 2816, 3328, 3840, 4352, 4864, 5376, 5888, 6400, 6561, 6912, 7424, 7936, 8448, 8960, 9472, 9984, 10496, 11008, 11520, 12032, 12544, 13056, 13122, 13568, 14080, 14592, 15104, 15616, 16128, 16640, 17152, 17664, 18176, 18688, 19200, 19712
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 1 - Product_{p prime} ((1 - 1/p) * Sum_{i>=1} 1/p^A004709(i)) = 0.002064412516... .
LINKS
EXAMPLE
256 = 2^8 is a term since 8 = 2^3 is not cubefree.
MATHEMATICA
noncubfreeQ[n_] := Max[FactorInteger[n][[;; , 2]]] > 2; Select[Range[2*10^4], AnyTrue[FactorInteger[#][[;; , 2]], noncubfreeQ] &]
PROG
(PARI) isnoncubefree(n) = {n > 7 && vecmax(factor(n)[, 2]) > 2; }
is(n) = {my(e = factor(n)[, 2]); for(i=1, #e, if(isnoncubefree(e[i]), return(1))); 0; }
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 03 2023
STATUS
approved