A361176 Numbers that are not exponentially cubefree: numbers with at least one noncubefree exponent in their canonical prime factorization.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A004709, A046099, A130897, A209061, A262276.

Sequence in context: A237008 A045057 A195091 * A203450 A188248 A253822

Adjacent sequences: A361173 A361174 A361175 * A361177 A361178 A361179

Keyword

nonn

Author

Amiram Eldar, Mar 03 2023

Status

approved